# Calc 2

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

1. No calculus need for this one. It's just a cylinder with a cone cut out.

r=1
h=4

v = πr^2h - π/3 r^2h = 2π/3 r^2h = 8π/3

Ok ok. If you want to use calculus, then with shells,

v = ∫[0,1] 2πrh dx
where r=x and h=y=4x
v = ∫[0,1] 2πx*4x dx = 8π/3

using discs (washers) you get

v = ∫[0,4] π(R^2-r^2) dy
where R=1 and r=x=y/4
∫[0,4] π(1-y^2/16) dy = 8π/3

posted by Steve
2. We have to use the Surface area of revolution formula

integral(f(x) aqrt(1+f'(x)^2))

posted by Melissa

## Similar Questions

1. ### 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.
2. ### 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
3. ### 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
4. ### 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
5. ### 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
6. ### Calculus

The region R is bounded by the x-axis, x = 1, x = 3, and y = 1/x^3. a.) Find the area of 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
7. ### Calculus

The region R is bounded by the x-axis, x = 1, x = 3, and y = 1/x3. a.) Find the area of 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
8. ### 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
9. ### 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
10. ### 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!!

More Similar Questions