# Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis. We have to use the surface area formula of revolution. Integral (2pi*f(x)sqrt(1+f'(x)^2))dx

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### Calc 2 Urgent Surface Area of Revolution Question

Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis. We have to use the surface area formula of revolution. Integral (2pi*f(x)sqrt(1+f'(x)^2))dx

### Calc 2 Urgent Surface Area

Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis. We have to use the surface area formula.

### Calculus HELP plz

Find the area of the surface obtained by rotating the curve y=sqrt(4x) from x=0 to x=1 about the -axis. about the x-axis. surface area= ⌠ 2pi * f(x)*sqrt[1 + (f'(x))^2] dx from a to b ⌡ it's been 45 years since I used that formula. I ended up with the integral of (...

### Math - Calculus

Find the area of the surface of revolution generated by revolving the curve y = 3 sqrt (x), 0 <= x <= 4, about the x-axis. Okay, so I've set up the integral like this: 2pi ∫[0,4] (3 sqrt (x))(sqrt(1+(1/4x)))dx Which is coming out to 108.5, but that's not giving me the ...

### Math (Calculus II) (Volume Revolution Setup)

Consider the graph of y^2 = x(4-x)^2 (see link). Find the volumes of the solids that are generated when the loop of this graph is revolved about (a) the x-axis, (b) the y-axis, and (c) the line x = 4. goo.gl/photos/v5qJLDztqsZpHR9d7 I'm just having trouble trying to set up the...

### Calculus II/III

A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the x-axis from 4 to 9. For part B of our question , the surface of revolution ...

### Math

Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: integral[4,1] sqrt(1+(dy/dx)^2) dy/dx = 1/2sqrt(x) (dy/dx...

### Calc 2

Find the area of the surface generated when y=4x and x=1 is revolved about the y-axis.

### Calculus

Suppose that the region between the x-axis and the curve y=e^-x for x>=0 has been revolved around the x-axis. Find the surface area of the solid. I got 3*pi The book shows an answer of pi * [sqrt(2) + ln(1 + sqrt(2))] Where do I go wrong? For the sides of the surface, I ...

### Calculus

Hello. I would appreciate it if someone could check my answers. I'm sorry it is so long. 1.) Let R denote the region between the curves y=x^-1 and y=x^-2 over the interval 1<= x <= 10. a. Set up an integral for the area of R. My answer: 1.403 b. Find x-bar, the x ...

### Math

I am in Calculus and am currently learning how to find the Area of a Surface of Revolution. I cannot understand what the surface of revolution (whether it's the x-axis, y-axis, or y=6) is. For example, I had a problem saying to use the washer method to find the volume of the ...

### Integral Calculus

Find the area of the surface generated by revolving the given curve about the y-axis. 8xy^2=2y^6+1 , 1<=y<=2. thank you so much.. :)

### Integral calculus

find the area of the surface generated by revolving about x-axis the upper half of the ellipse 4x^2 + 16y^2 = 64

### asdf

Find a definite integral indicating the area of the surface generated by revolving the curve y = 3√3x ; 0 ≤ y ≤ 4 about the x – axis. But do not evaluate the integral.

### Calculus check and help

Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. Find the the area of R. B. Find the value of z so that x=z cuts the solid R into two parts with equal area. C. Find the...

### math

Okay. So i'm doing this project for my geometry class about different sports, soccer, baseball, basketball, bowling, golf, volleyball and pool. I have to find the surface area, volume, diameter, circumference, and radius of each of the balls. I got a circumference for each one...

### Calculus

This is the questions I have trouble with : Set up (do not evaluate) the integral that gives the surface area of the surface generated by rotating the curve y=tanhx on the interval (0, 1) around the x-axis. Anyone who can help? Not really sure how to even begin! Thanks

### integral calculus

find the volume of the solid generated by revolving the area by the given curves about the indicated axis of revolution y^2=4ax,x=a;about the y-axis

### integral calculus

find the volume of the solid generated by revolving the area by the given curves about the indicated axis of revolution y^2=4ax,x=a;about the y-axis.

### calculus II SURFACE AREA Integration

Find the exact area of the surface obtained by rotating the curve about the x-axis. y = sqrt(1 + 5x) from 1 ≤ x ≤ 7

### Calc

Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the y-axis. y = cube rt. (x) + 2 Thank you so much!!

### University Calculus

Set up (do not evaluate) the integral that gives the surface area of the surface generated by rotating the curve y=tanhx on the interval (0, 1) around the x-axis. Anyone who can help? Not really sure how to even begin! Thanks

### Calculus

Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: âˆ«[4,1] sqrt(1+(dy/dx)^2) dy/dx = 1/2sqrt(x) (dy/dx)^2...

### calculus 2

The curve y=sinh(x),0<=x<=1, is revolved about the x-axis. Find the area of the resulting surface.

### Calculus

Find the exact coordinates of the centroid. y = sqrt[x], y = 0, x = 9. -------------- Is this basically 1/4 of an oval/ellipse? If so then the area would be: pi*9*3, correct? So the X coordinate would equal: 1/Area * Integral from 0 to 9 of (x*f(x))*dx Which equals: (4/(27*pi...

### math

how would you find the surface area of a cylinder with 1.7m for the diameter, and 3m for the height? would you use the formula S.A = 2pi x r x h, or S.A = area of two congruent circles + area of rectangle?

### Calc

Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the x-axis. y = (x³/6) + (1/2x), 1≤ x ≤ 2

### Calculus

Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2, x=0, and y=0 (a) integral (x^2)^2 from 0 to 2=32/5...

### Calculus

Determine the volume of the solid abtained when the region bounded by y=sqrt x and the line Y=2 and x=0 is rotated: (i) about the x-axis (ii) about the line x=4. (i) Each element of the body of revolution with thickness dx, has area pi*(sqrt x)^2 dx = pi x dx. Integrate that ...

### Calculus

The region enclosed by the graph of y = x^2 , the line x = 2, and the x-axis is revolved abut the y-axis. The volume of the solid generated is: A. 8pi B. 32pi/5 C. 16pi/3 D. 4pi 5. 8pi/3 I solved for x as √y and set up this integral: 2pi * integral from 0 to 2 of y√y. But ...

### Math Homework

1) Given the side of a square pyramid is 6cm and the altitude is 4cm calculate the surface area. 2) Given the side of a square pyramid is 12cm and the altitude is 8cm calculate the surface area. 3) Given the side of a square pyramid is 18cm and the altitude is 12cm calculate ...

### Algebra 1

Earth has a radius of about 6.4 x 10 to the 6th power m. Approximate the surface area of earth using the formula for the surface area is a sphere, S = 4 pi r squared. Earths surface is about 70 percent water. About how many square meters of earths surface are covered with ...

### calculus

Find the surface area of the solid generated by rotating the area between the y-axis, (x^2/y) + y = 1, and -1≤y≤0 is rotated around the y-axis.

### Calculus

Hello, I would like to make sure the answers to these questions are correct. 1. Using the shell method, what is the volume of a solid that is generated by rotating the region by y = x^2 and x = y^2 about the x axis. My Work: r = y h = sqrt(y) - y^2 2pi ∫[0,1] (y)((sqrt(y) - ...

### Functions, graphs

f(x)=(x+1)/(1+x^2) a) explain why the graph lies above the x axis on the interval x=0 and x=sqrt(3) b)write an expression using the indefinite integral that gives the area between the graph f and the x axis between the values x=0 and x=sqrt(3). c)use integration to find the ...

### CALCULUS problem

There are four parts to this one question, and would really appreciate if you could show and explain how you get to the answer, because I tried looking up how to find the answer myself, but nothing made sense. Thank you! 11. The region R is bounded by the x-axis, x = 1, x = 3...

### calculus

Surface area of revolution y=(x^3)+3 about the x-axis from (0,1)

### math(again)

the ? says "a cone has the surface area of 160 sq. in. If the dimensions are reduced by 1/2,what is the surface area of the new cone?" i just cant seem to find the formula for the surface area of the cone.

### Calculus I

Find the exact area of the surface obtained by rotating the curve about the x-axis. y = sqrt(1+5x) from 1<x<7

### Calculus I

Find the exact area of the surface obtained by rotating the curve about the x-axis. y = sqrt(1+5x) from 1<x<7

### Calculus

alright. i need to write a definite integral for the volume and evaluate the integral for the region bounded by y=x^2, y=0, and x=1 revolved about the a) x-axis, b) the y-axis, c) x=2, and d) y=-2. HELP! Lets do the x=2 axis. dV= pi rh dr where r is radius, h is height. r= x-1...

### Calculus (Solid of Revolution)

The region R is bounded by the x-axis, x = 1, x = 3, and y = 1/x^3. C. Find the volume of the solid generated when R is revolved about the x-axis.

### Math--Volume and Surface Area

The volume of a cube is 125 cubic inches. Find the surface area. I know that the volume formula is V=Bh where v=volume, B=area of the base, and h=height. How do I get the surface area though? Also, The surface area of a cube is 384 square cm. Find the volume. I think it's ...

### Math

I am doing a project, are my answers correct? 1. Find and simplify the volume-to-surface-area ratio for each of the three possible ice cube shapes. You can use this chart. |Shape| S/A Formula|Volume Formula Cube | S.A=6s^2 | V=s^3 6/s Sphere|S.A+4 pi r^2|V=4/3 pi r^3 3/r ...

### Integral calculus

Use the cylindrical shell method to find the volume of the solid generated by revolving the area bounded by the given curves (x-3)^2 + y^2 = 9, about y-axis.

### Calculus

This is a question from my textbook that does't have a solution and quite frankly I have no idea what to do. Any tips would be greatly appreciated. Given the function f defined by f(x) = 9 - x^2. Find the surface area bounded by the curve y = f(x), the x axis and the lines x...

### Math

Find the area of the surface generated by revolving the curve y = (x + 3)^1/2, 2 ≤ x ≤ 4 about the x-axis.

### calc: relative error

The circumference of a sphere was measured to be 77 cm with a possible error of .8 cm. Use differentials to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface area. please help me..thank you! Area= 4 PI radius^2 dA...

### Chemistry

Compute the surface area of revolution about the x-axis over the interval. y = x^2, [0, 4] Is it (pi/12)(65^2 - 65)^(3/2)?

### Calculus

Compute the surface area of revolution about the x-axis over the interval. y = x^2, [0, 4] Is it (pi/12)(65^2 - 65)^(3/2)?

### MATH

Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the following about the given axes. x = y - y3, x = 1, y = 1 (b) Revolved about the y-axis ? Hi Shawn, 97/105 * pi ? :) We need to cut away the volume of the region you get by ...

### calculus

Find the surface area generated when y = (x^3/12) + (1/x), from x=1 to x=2 is rotated around the x-axis.

### calc

1. Let R be the region bounded by the x-axis, the graph of y=sqr(x) , and the line x=4 . a. Find the area of the region R. b. Find the value of h such that the vertical line x = h divides the region R into two regions of equal area. c. Find the volume of the solid generated ...

### Calculus check

The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-2x. Let R be the region bounded by the x-axis and the graphs of f and g. A. Find the area of R. B. The region R from x=0 to x=4 is rotated about the line x=4. Write, but do not evaluate, an integral expression the ...

### Calculus

Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. Find the the area of R. B. Find the value of z so that x=z cuts the solid R into two parts with equal area. C. Find the...

### Math

Find the volume of the solid generated by revolving the region bounded by y=x+(x/4), the x-axis, and the lines x=1 and x=3 about the y-axis. I've drawn the graph and I understand which part is being rotated, but I'm having trouble setting up the equation. Because there is a ...

### Calc

Find the exact total of the areas bounded by the following functions: f(x) = sinx g(x) = cosx x = 0 x = 2pi I set my calculator to graph on the x-axis as a 2pi scale. The two functions appear to cross three times between x = 0 and 2pi. (including 2pi) Now, from top to bottom, ...

### Calculus

The graph of the curve y2=10 x+10 is a parabola, symmetric with respect to the x-axis. Find the area of the surface generated by rotating about the x-axis the part of this curve corresponding to 0 ≤ x ≤ 20.

### Calculus

*Note I reposted this question as I changed the subject** The Region "R" under the graph of y = x^3 from x=0 to x=2 is rotated about the y-axis to form a solid. a. Find the area of R. b. Find the volume of the solid using vertical slices. c. Find the first moment of area of R ...

### Math - Geometry

A cylindrical solid has a cylindrical circular hold drilled out of the center. Bascially, it's a circular cylinder with a hollow spot right down the middle. Find the surface area of the resulting solid. radius of larger circle: 2in radius of smaller circle (hollow area): 1in ...

### Geometry / Math

Hi guys I need help ASAP, I have tried every thing I know about math and I cant figure any of them out. Thank you... _________________________________ 1. Use a formula to find the surface area of the square pyramid. (H.6ft.)(W.3ft.)(L.3ft.) A. 45 ft B. 81 ft*** C. 36 ft D. 72 ...

### MATH

Hi guys I need help ASAP, I have tried every thing I know about math and I cant figure any of them out. Thank you... _________________________________ 1. Use a formula to find the surface area of the square pyramid. (H.6ft.)(W.3ft.)(L.3ft.) A. 45 ft B. 81 ft*** C. 36 ft D. 72 ...

### MATH-Stuck

For each of the following, the Surface Area is given. Calculate the missing dimension. This is a rectangular prism with the width missing. The height seems to be 20 cm. The length I guess is 34 cm, and the Surface Area is 6020cm square. How do I find the missing width? I ...

### First Moment

The Region "R" under the graph of y = x^3 from x=0 to x=2 is rotated about the y-axis to form a solid. a. Find the area of R. b. Find the volume of the solid using vertical slices. c. Find the first moment of area of R with respect to the y-axis. What do you notice about the ...

### maths

A metal pipe is 63cm long. Inner diameter of a cross section is 6m and the outer diameter is 8cm find:-surface area of the base a , surface area of the base b , the outer curved surface area inner curved surface area total surface area

### Math

Find the surface area of rectangular pyramids 1. Length= 1.15ft Width=0.82 ft Height of the slanted face =3.17ft Surface Area=7.1879ft^2 Formula for Rectangular Pyramid Surface Area : B+1/2pl B=area of base p=perimeter of base l=height of slanted face

### Calculus Homework

You are blowing air into a spherical balloon at a rate of 7 cubic inches per second. The goal of this problem is to answer the following question: What is the rate of change of the surface area of the balloon at time t= 1 second, given that the balloon has a radius of 3 inches...

### Calculus

The semicircular region bounded by the curve x=sqrt{9-y^2} and the y-axis is revolved about the line x=-3. The integral that represents its volume is V= âˆ« [a^b] f(y) dy What is f(y)? I've gotten f(y) to: (1+(sqrt(9-y^2)))^2-9 But it's not being accepted. What am I doing ...

### calculus

Hi, I have the following HW question and I'm a little confused: Find the volume of the solid generated by revolving the region bounded by y=1/sqrt(x) and y=0 for 1 <= x <= 2 about the line y=-1. So far I have the integral 2pi (-1-y)(1-1/y^2) dy from -1 to 1, but that's ...

### Geometry / Algebra 1

(a) The surface area of the prism shown is 314 square meters. Write an equation that u can solve to find the value of w. side a=wm b=8m and c=(w+4)m (on the picture) I'm guessing u use the formula surface area=2ab+2bc+2ac??? Well if so I need all that solved into y=ax*2+bx+c ...

### calculus

Given the area is in the first quadrant bounded by y²=x, the line x=4 and the 0X What is the volume generated when this area is revolved about the 0X? the answer is 25.13 but I don't know how. help me please

### Geometry

When finding the surface area of a composite figure, which in this case consists of a square pyramid sitting on top of a cube, I know that the first step is to find the surface area of the cube, but after that I would find the surface area of the square pyramid, but do I ...

### Calc 3 Surface Area

Find the surface area of the indicated surface. 1.) The Portion of z=4y+ 3x^2, between y=2x, y=0 , and x=2 2.) The Portion of z= x^2 + y^2, below z=4 . 3.) The portion of z= sqrt(x^2 +y^2) between y=x^2 and y=4. 4.) The portion of 2x+y+z=8 in the first octant. Any help with ...

### Pre-Calculus

The surface ares S (in square meters) of a hot air ballon is given by s(r)=4 pi r^2 where r is radius of balloon (in meters). If the radius r is increasing with time (in seconds) according to the formula r(t) = 2/3t^3, t is greater than or equal to 0, find the surface area S ...

### Calc

Consider the Dosage Formula y=(S/1.73 where y = childfs dosage, a = the adult dosage, and S = the surface area of the body in square meters. The Surface Area Formula is S(w,h)=0.0101w^(.425)*h^(.725) where S = the surface area of the body in square meters, w = the weight in ...

### CALCULUS

The region R is bounded by the x-axis, y-axis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the x-axis. C. The solid formed in part B is divided into two solids of equal volume by a plane ...

### math-PLEASE CHECK

Find the surface area and volume of each of the following figures: d.Right circular cylinder v=pir^2h pi(3)(3)(6) pi(54) v=169.6 cubic cm sa=2pi r^2 + 2pi rh 2pi(3)(3)+2pi(3)(6) 2pi(9)+2pi(18) 56+113=169 Sa=169 square cm is this right???

### CALCULUS HELP PLZ

The region R is bounded by the x-axis, y-axis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the x-axis. C. The solid formed in part B is divided into two solids of equal volume by a plane ...

### Math, Please check answers

I do not want to fail this, could you please help me with number 1 and 3.D, and then check my other answers? Thank you. 1. Find and simplify the volume-to-surface-area ratio for each of the three possible ice cube shapes. You can use this chart. |Shape| S/A Formula|Volume ...

### Math

A roll of paper towels is 10 inches high and 2.5 inches in diameter. How many full squares inches of paper towel can fit on the roll in 15 rotation? * all I need is a formula of this question. Do I use lateral surface area formula or total surface area formula

### maths

the ratio of total surface area to the curved surface area of a right circular cylinder is 3:2 find the volume if its total surface area is 14784 cm2

### Calculus II: Shell Method for finding volumes

Question: What is the volume of the revolution bounded by the curves of y=4-x^2 , y=x, and x=0 and is revolved about the vertical axis. First, I had found the points of intersection to get the limits and I got -2.5616 and 1.5616. And then I plug it in the shell method formula ...

### algebra1 HELP PLEASE

Mary is making a pinata that has a ball-like shape. The pinata has a surface area of 50 square feet. Use the formula for the surface area of a sphere: to find the radius of the pinata. Round your answer to the nearest hundredth. _____ feet

### algebra1 HELP PLEASE

Mary is making a pinata that has a ball-like shape. The pinata has a surface area of 50 square feet. Use the formula for the surface area of a sphere: s=4(pi)^2 to find the radius of the pinata. Round your answer to the nearest hundredth. _____ feet

### Math 2

Use the diagram to find the surface area of a triangular prism. Find the area of the two triangular faces. Then find the area of each of the three rectangular faces. What is the surface area? Describe how you solved the problem. Prism has numbers of 4, 3, 6 and 5. And teacher ...

### Geometry

What is the lateral surface area of the prism? Rectangular prism Length: 17.2 Width: 3 Height: 5.5 283.8 m^2 292.4 m^2 325.4 m^2 407 m^2 I already found the surface area (325.4 m^2) and I'm using the formula for lateral surface area 2lh + 2wh... but I keep getting 222.2 which ...

### Calculus - Center of Mass

Find the exact coordinates of the centroid given the curves: y = 1/x, y = 0, x = 1, x = 2. X = 1/Area*Integral from a to b: x*f(x)dx Y = 1/Area*Integral from a to b: [(1/2)*(f(x))^2]dx How do I find the area for this? Once I know that, is this the correct set up? X = 1/Area*...

### Algebra II

12. A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4 r2 for the surface area of a sphere. (1 point) 64 x2 + 32 x + 4 64 x2 + 16 x + 4 *my answer 4 x2 + 32 x + 64 4 x2 + 4

### algebra--1 question

A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4(pi)r^2 for the surface area of a sphere. 16(pi)x^2 + 16(pi) 16(pi)x^2 + 48(pi)x + 16(pi) 36(pi)x^2 + 48(pi)x + 16(pi) 36(pi)x^2 + 24(pi...

### Calculus

if the surface area of a sphere is given by the formula SA=4pir^2, find the rate of increase of the surface area if the radius is 4 cm and is increasing at the rate of 0.5 cm/min.

### maths

b) if the surface area of the base is increased by times its original surface area,(with the same vertical height),calculate the new surface area of the pyramid.

### Algebra

A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4(pi)r2 for the surface area of a sphere.

### calculs

Find the volume when the plane area bounded by y=-x^2-3x+6 and x+y-3=0 is revolved about (1) x=3 and (2) about y=o B. Find the volu6 of focus generated by revolving the circule x^2+y^2=4 about the line x=3

### math

The surface area of spherical ball of radius r is given by the formula S=4(22/7)r2. Find surface area of ball of diameter 12cm.

### Calculus check and help

Let R be the region bounded by the curves y=lnx^2 and y=x^2-4 to the right of the y-axis. A. Find the area of R. B. Find the folume geneated when R is rotated about the line y=-4. C. Write, but do not evaluate the integral expression that gives the volume of the solid ...

### Integral Calculus

Volume of the area bounded by y=sin(x), x-axis, x is greater than or equal to 0 but less than or equal to pi, revolved about x=3pi/2.

### math/science

The total surface area of Earth is about 1.97 × 10^8 square miles. The surface area of land on Earth is about 5.73 × 10^7 square miles. Find the ratio of surface area of land to that of the entire planet.

### Calculus

The question is find the area of the reagion that is bounded by the curve y=arctan x, x=0, x=1, and the x-axis. So I've drawn the enclosed region. To find the area would I use the Disc/shell method? If so the formula that I came up with looks like this: If area = pi(r)^2 then ...

### algebra1please look over THANK YOU

Mary is making a pinata that has a ball-like shape. The pinata has a surface area of 50 square feet. Use the formula for the surface area of a sphere: s=4(pi)^2 to find the radius of the pinata. Round your answer to the nearest hundredth. _____ feet i got 50=39.4 but don't ...