# the total surface area of a right circular cone is 90pi. its radius is 5. what is the volume of the cone?

84,097 results

### Math

A cone is formed from a sector of a circular of radius 9cm which sustained an angel 120 find (a) the radius of the cone formed (b) the curved surface area of the cone (c) the total surface (d) volume

### Calculus

Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to have the largest possible volume, what fraction...

### math

Consider the right circular cone shown. If the radius of the circular base remains the same and the height varies, what are the minimum surface area and minimum volume the cone can have?

### math

Consider the right circular cone shown. If the radius of the circular base remains the same and the height varies, what are the minimum surface area and minimum volume the cone can have?

### math

Consider the right circular cone shown. if the radius of the circular base remains the same and the height varies, what is the minimum surface area and minimum volume the cone can have?

### Calculus: Optimization

I have no idea how to approach this problem, if someone knows just how to relate h, r with H,R, that would be extremely helpful and I can workout the rest! Thank you in advance. Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the ...

### Maths

A right circular cone is circumscribed about a sphere of radius a .If h is the distance from the centre of the sphere to the vertex of the cone. Show that the volume of the cone is 1/3pi a^2(a+h)^2/(h-a). Find the angle of a cone when the volume is minimum

### math

Two right circular cone, one upside down in the other. The two bases are parallel. The vertex of the smaller cone lies at the center of the larger cone’s base. The larger cone’s height and base radius are 12 and 16 ft, respectively. What are the smaller cone’s height (h...

### Calculus

A right circular cone is inscribed in a sphere of radius r. Find the dimensions of the cone that maximize the volume of the cone.

### Calculus

A right circular cone is inscribed in a sphere of radius r. Find the dimensions of the cone that maximize the volume of the cone.

### Math

What is the surface area and volume of a composite figure made up of a hemisphere and a cone in terms of pi? The radius is 10, and the slant height is 15. Are my answers right? Cone surface area: π(10)(15) = 150π Hemisphere surface area: 2π(10)^2 = 200π 350...

### MATH214

Find the surface area of a right circular cone topped with a hemisphere. the height of the cone is 8cm, the radius is 4cm.

### MATH214

Find the surface area of a right circular cone topped with a hemisphere. the height of the cone is 8cm, the radius is 4cm.

### maths --plse help me..

Prove that the radius of the base of right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half that of the cone

### math class viii

Q.1) The volume of a right circular cone is 37.68 dm3 .If the the base is 3 dm, find (1) the height (2) the curved surface area of the cone .( Take π=3.14)

### math

A right circular cone stands on a hemisphere. The base radius of the cone is equal to the radius of the hemisphere. If the base radius of the cone is 10 centimeters and its height is 15 centimeters,calculate the total volume of the solid.

### math

A right circular cylinder of radius r and height h is inscribed in a right circular cone of radius R and height H, as shown on the right figure. Find the value of r (in terms of R and H) that maximizes the total surface area of the cylinder (including top and bottom). Comment ...

### math

A right circular cone is inscribed inside a sphere. The right circular cone has the radius of the base of 4 inches and the height is greater than 2 inches. The sphere has a radius of 5 inches. What is the ratio of the volume of the cone to the volume of the sphere? Leave your ...

### maths

A Toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere .If the radius of base of the cone is 21 cm and its volume is 2/3 of the volume of hemisphere calculate the height of cine and surface area of the toy.

### geometry

The surface area of a cone is 38 in^2. The radius of a similar cone is triple the radiusof the orginal cone. What is the surface area of the new cone?

### Math

An inverted right cone, half filled with water. I've only the volume of the entire cone to go from. So the volume of the cone = 1/3 the base area * height I've been told by a friend that the base area of a half scale cone = 1/4 of the larger cones base area; with the height ...

### Math

A right pyramid has a surface area of 258 cm2. A right cone has a base radius of 4 cm. The cone and pyramid have equal surface areas. What is the height of the cone to the nearest tenth of a centimetre?

### Math 130

Jodi says that if you double the radius of a right circular cone and divide the slant height by 2, then the surface area of the cone stays the same since the 2s cancel each other out. How do you respond?

### Math

the formula for the volume of a cone is v=1/3pir^2h. The volume cone x is 2 times the volume of cone Y. Why the height of cone X is 2 times the heigh of the cone Y, and the radius of cone X is the same as the radius of cone Y.

### Surfaces of cones

The diameter of the base of the cone is 24x cm. The height of the cone is 16x cm. The curved surface area of the cone is 2160pi cm^2. The volume of the cone is V pi cm^3, where V is an integer. What is the value of V. Answer is cm^2. Thanks a lot.

### 7th g-math

An ice-cream shop offers a small size cone and a large size cone. The height of the large cone is 2 times the height of the small cone. The radius of the large cone is 2 times the radius of the small cone. Which statement is true about the volumes of the two cones? A. The ...

### math geometry

A right circular cone has a base diameter of 10 and a height of 18. A second right circular cone has a base diameter of 15. If the volume of the second cone is equal to the volume of the first cone, then what is the height of the second cone? provide complete solution w ...

### geometry

A cone is topped with a hemisphere. Calculate the total surface area if the radius of the cone and hemisphere is 10 cm and the height of the cone is 24 cm.

### Calculus

A cone is inscribed in a sphere of radius a, centred at the origin. The height of the cone is x and the radius of the base of the cone is r, as shown in the diagram opposite. Find the height, x, for which the volume of the cone is a maximum. (HINT: show that the volume of the ...

### Math 214

How do you find the volume of a right circular cone with a hemisphere? The height of the cone is 8 cm and the radius in 4cm.

### Maths

(1) A cone has height of 8cm and circular radius 6cm calculate (a) It's Volume (b) It's Slant Height (c) The Curved Surface Area (d) The Total Surface Area

### calculus

Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to have the largest possible volume, what fraction...

### geometry

A right circular cone is made from of a radius of 5 cm, a central angle of 216 degrees, what is the volume of the cone in cubic cm?

### MATHEMATICS

Find the curved and total surface area of a right circular cone,of base radius 8cm and height 10cm

### Math

A sphere is inscribed in a right cone. The slant height of the cone = the diameter of the base of cone. If the radius of the sphere is r, find the volume of the cone in terms of r.

### calculus

A paper cone is to be formed by starting with a disk of radius 9cm, cutting out a circular sector, and gluing the new edges together. The size of the circular sector is chosen to maximize the volume of the resulting cone. How tall is the cone?

### calculus

A paper cone is to be formed by starting with a disk of radius 9cm, cutting out a circular sector, and gluing the new edges together. The size of the circular sector is chosen to maximize the volume of the resulting cone. How tall is the cone?

### calculus

A paper cone is to be formed by starting with a disk of radius 9cm, cutting out a circular sector, and gluing the new edges together. The size of the circular sector is chosen to maximize the volume of the resulting cone. How tall is the cone?

### math

The height of a right circular cone is decreased by 6 percent. Find the percentage that the radius of the base must be decreased by so that the volume decreases by 20 percent. Recall that the formula for the volume of a right circular cone is V = πr2h 3

### MATHEMATICS

A SECTOR IS USED TO FORM ACONE IF THE RADIUS AND ANGLE OF THESECTOR IS 8CM AND 160 DEGREE RESPECTIVELY CALCULATE, THE RADIUS OF THE CONE ,VERTICAL HEIGHT, VERTICAL ANGLE, VOLUME AND TOTAL SURFACE AREA OF THE CONE

### calculus

A right triangle with hypotenuse 5 inches is revolved around one of its legs to generate a right circular cone. Find the radius and height of the greatest volume cone.

### maths

Two spheres of radius 6 cm and 4cm are inscribed in a right circular cone.The bigger sphere touches the smaller one and also the base of cone .find the height of the cone?

### Geometry

A cone with a radius of 3 inches has a total area of 24 pi sq in. Find the volume of the cone.

### geometry

A cone has a volume of 36pi cubic meters. Its height is four times its radius. Find the surface area of the cone.

### Calculus

Show that a right-circular cylinder of greatest volume that can be inscribed in a right-circular cone that has a volume that is 4/9 the volume of the cone. Please, help out, this is for a study guide for a quiz. :) Thank you.

### geometry

11. Infinitely many different sectors can be cut from a circular piece of paper with a 12-cm radius, and any such sector can be fashioned into a paper cone with a 12-cm slant height. (a) Show that the volume of the cone produced by the 180-degree sector is larger than the ...

### Geometry

Infinitely many different sectors can be cut from a circular piece of paper with a 12-cm radius, and any such sector can be fashioned into a paper cone with a 12-cm slant height. (a) Show that the volume of the cone produced by the 180-degree sector is larger than the volume ...

### maths-surface area

A solid is in the form of cone mounted on a hemisphere in such a way that the centre of the base of the cone just coincide with the centre of the base of the hemisphere. Slant height of the cone is L and radius of the base of the cone is 1/2r where through r is the radius of ...

### Maths

A right circular cone of base radius 5 cm and depth 20 cm is held with its vertex downwards. If water is leaking through a small hole in the vertex at the rate of 8 cm^3/s, find the rate of change of the water level in the cone when the radius of the water surface is 4cm, ...

### math

the radius r of a right circular cone is increasing at a rate of 2cm/min.the height h of the cone is related to the radius by h=3r.find the rate of change of the volume when r=6cm

### geometry math

There is an upside-down cone that is 12m high and has a circular base with a radius of 4m that is being filled with liquid. Make V, the volume, a function of the height of the liquid, h. What is the volume of the cone when the water is 5m deep? V = (1/3)pi*r^2*h This formula ...

### math

a right triangle whose hypotenuse is h mm long is rotated about one of its legs to generate a circular cone.find the radius and altitude of the cone of greatest volume.

### 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.

### math

If you are calculating surface area of a right circular cone topped with a hemisphere. the radius is 4 cm and the rt angle is 8 cm...what is the lateral surface area. Is it 8.94 or is it 9? Explain answer please. Thanks

### ap Calculus

A right circular cone has a fixed slant height, s= 12 inches. Determine the radius and the height of the cone with maximum volume

### Calculus

Find the radius, volume, and hieght of the right- circlar cylindar that can be inscribed in a right- circular cone with a radius of 6 inches and a hieght of 10 inches. There are an infinite number of solutions to this. Did you mean the right cylinder with the max volume? Or ...

A right circular cone has a volume of 140 in^3. The height of the cone is the same length as the diameter of the base. Find the radius and height.

### math

The base radius of a cone is 6 inches, and the cone is 8 inches tall. To the nearest square inch, what is the area of the lateral surface of the cone?

### math

The base radius of a cone is 6 inches, and the cone is 8 inches tall. To the nearest square inch, what is the area of the lateral surface of the cone?

### math

A right circular cone has a base diameter of 10 and a height of 18. A second right circular cone has a base diameter of 15. If the volume of the second cone is equal to the volume of the first cone, then what is the height of the second cone?

### Math

Completely bemused, do not know how to get the answer. a)8π b)7√2 c)27√π d)7√×7√×1 13- Determine the exact total surface area of a sphere with radius 2√2 metres. a) An inverted cone with side length 4 metres is placed on top of the ...

### Algebra

Find the surface area of a right circular cone with radius of 5cm and height of 12cm.

### Maths

A hemispherical paper is folder into a hallow right circular cone. The radius of the hemispherical paper is 12cm. What's the cone's base radius, height and volume?

### math

A paper cone has a base diameter of 8cm and a height of 3cm a. Calculate the volume of the cone in term of pie b. Calculate the curve surface area of the cone

### mathe

Show that a right-circular cylinder of greatest volume that can be inscribed in a right-circular cone that has a volume that is 4/9 the volume of the cone.

### Math

Find the radius of a right circular cone if its volume is 1.5 times its lateral area and its radius is half its slant height.

### math

a cone has a circular base of radius 16cm and a volume of 420cm2.find the height of the cone.

### math

a cone has a circular base of radius 16cm and a volume of 420cm2.find the height of the cone.

### algebra

A candle in the shape of a circular cone has a base of radius r and a height of h that is the same length as the radius. Which expresses the ratio of the volume of the candle to its surface area(including the base)? For cone, V=1/3pir^2h and SA=pir^2+pir sqrt r^2 +h^2. Think ...

### Geometry

One right circular cone is set inside a larger circular cone. The cones share the same Axis, the same vertex, and the same height. Find the volume of the space between the cones of the diameter of the inside cone is 6in., the diameter of the outside cone is 9in and the height ...

### math

Suppose we pump water into an inverted right-circular cone tank at the rate of 6 cubic feet per minute. The tank has the height 9 ft and radius on the top is 8 ft. What is the rate at which the water level is rising when the water is 3 ft deep? Leave the answer approximate. ...

### Geometry

The surface area of the right circular cone topped with hemisphere is? 2cm radius and 4cm height

### Math

A right circular cylinder with a height of 20 cm and a right circular cone share a circular base and have the same volume. What is the height of the cone?

### Algebra 1--How Am I Supposed to Solve This?!

Suppose a cone and a cylinder have the same radius and that the slant height l of the cone is the same as the height h of the cylinder. Find the ratio of the cone's surface area to the cylinder's surface area. Area of cone: S = πrl + πr^2 Area of cylinder: S = 2π...

### Calculus

Approximate the change in the lateral surface area(excluding the area of the base) of a right circular cone fixed height of h = 6m when its radius decreases from r=9m to r=8.9m (S=(pi)r sqrt(r^2+h^2)).

### ALGEBRA 2 HONORS

A container is to be made in the shape of a cylinder with a conical top. The lateral surface areas of the cylinder and cone are S1 = 2(pi)rh and S2 = 2(pi)r√(r^2 + h^2). The surface area of the base of the container is B= (pi)r^2. The height of the cylinder and cone are ...

### math

The volume of a cone is given by the formula V = (1/3)r2h. A cone has a volume of 11,907 cm3 and a radius of 21 cm. what would be the height of the cone.

### Calculus

approximate the change in the lateral surface area(excluding the area of the base of a right circular cone of fixed height of h=6m when its radius decreases from r=11m to r=10.9m S=(pi)r sqrt(r^2+h^2)

### Geometry

A cone has diameter 12 and height 9. A cylinder is placed inside the cone so the base of the cylinder is concentric with the base of the cone and the upper base of the cylinder is contained in the surface of the cone. If the volume of the cone is nine times the volume of the ...

### Geometry

A cone has diameter 12 and height 9. A cylinder is placed inside the cone so the base of the cylinder is concentric with the base of the cone and the upper base of the cylinder is contained in the surface of the cone. If the volume of the cone is nine times the volume of the ...

### Maths

If a cone of radius r and slant height 2r is surmounted on a cone having radius 2r and slant height 4r then find total surface area of solid

### Geometry

"A cone has the radius of 24 and its volume is 1,920 what is the volume of a similar cone with the radius of 18 Answers A.480 B.810 C.1,080 D.1,440" How do I find the height for the similar cone to get its volume?

### Calculus

A right circular cone has a constant slant height of 12 feet. Find the radius of the base for which the cone has maximum value

### Pure Maths

A container is in the shape of a right circular cone (inverted) with both height and diameter 2 meters. It is being filled with water at a rate of (pi)m^3 per minute. Fine the rate of change of height h of water when the container is 1/8th full(by volume). (Volume of a right ...

### Math, Calculus

A right circular cone has a constant slant height of 12 feet. Find the radius of the base for which the cone has maximum value

### Maths

“A solid consists of a right circular cylinder surmounted by a cone of the same diameter. If the height of the cone is 'h' and the volume of the solid is 3 times the volume of the cone , then find the height of the cylinder.”

### calculus

A right triangle of hypotenuse L is rotated about one of its legs to generate a right circular cone find the largest volume that such a cone could occupy

### calculus

A right triangle of hypotenuse L is rotated about one of its legs to generate a right circular cone find the largest volume that such a cone could occupy

### Geometry 10th

A cone is inscribed in a sphere with a radius of 5 centimeters.The distance from the center of the sphere to the center of the base of the cone is x. Write an expression for the volume of the cone in terms of x (Hint: Use the radius of the sphere as part of the height of the ...

### PreCalculus

Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), cut out a sector with an arc of length x. Join the two radial edges of the remaining portion of the paper to form a cone with radius r and height h, as shown in (b). What length of ...

### Math

Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), cut out a sector with an arc of length x. Join the two radial edges of the remaining portion of the paper to form a cone with radius r and height h, as shown in (b). What length of ...

### Math

Please Help A body consists of a solid hemisphere of radius r joined to a right circular cone of base radius r and perpendicular height h. The plane surfaces of the cone and hemisphere coincide and both solids are made of the same material. Show that the centre of gravity of ...

### geometry: volume of cone

If the radius of a cone is cut in half, the volume of the cone is multiplied by what number?

### geometry

The volume of a cone is 54 pi cubic inches. The radius and height of the cone are both reduced by a factor of 3 to create a new cone. What is the volume of the new cone? Is the volume of the new cone 18pi cu in A. 2 pi cu inches B. 6 pi cu inches C. 9 pi cu inches D. 18 pi cu ...

### Algebra

The volume of a cone is 54 pi cubic inches. The radius and height of the cone are both reduced by a factor of 3 to create a new cone. What is the volume of the new cone? Is the volume of the new cone 18pi cu in A. 2 pi cu inches B. 6 pi cu inches C. 9 pi cu inches D. 18 pi cu ...

### Math

A cone is constructed by cutting a sector from a circular sheet of metal with radius 20cm. The cut sheet is then folded up and welded. Find the radius and height of the cone with the maximum volume that can be formed in this way.

### CALC HELP ASAP

suppose you need to construct a cone who surface area is 100 sq in. (A= pi*r*(sqrt( r^2+h^2), this is the amount of carboard needed to construct the cone. find values of r and h that will maximize the volume of the cone (V= (pi/3)r^2h Please help. explanations and steps please...

### math

a cone has a height of 6.if the volume of the cone is 24xpi, what is the radius of the cone?

### Math

Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 feet high? Recall that ...

### calculus

Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 24 feet high? Recall that...