Question

What is the volume of a cylinder if it has the same area and height of a cone with a volume of 36pi

Answer 1

The volume of the cylinder is 108 π units³

Explanation:

• The formula of the volume of the cone is V =
  `(1)/(3)` πr²h, where r is the radius of its base and h is its height
• The formula of the volume of a cylinder is V = πr²h, where r is the radius of its base and h is its height

∵ The area of the base of the cylinder is equal to the area of

the base of the cone

∴ Their radii are equal

∵ The height of the cylinder is equal to the height of the cone

∵ The volume of the cone = 36 π units³

- Equate the formula of the volume of the cone by 36 π

∵ 36 π =
`(1)/(3)` πr²h

- Multiply both sides by 3

∴ 108 π = πr²h

- Divide both sides by π

∴ 108 = r²h

- Substitute the value of r²h in the formula of the volume of

the cylinder

∵ V = πr²h

∴ V = π (108) = 108 π

∴ The volume of the cylinder is 108 π units³