Question

A cylinder and a cone have the same volume. The cylinder has a radius of 2 inches and a hieght of 3 inches. The cone has a radius of 3 inches. What is the hieght of the cone?

Answer 1

The height of the cone is inches, if the cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.

Explanation:

The given is,

A cylinder and a cone have the same volume

Cylinder has a radius 2 inches and height of 3 inches.

Cone has a radius of 3 inches

Step:1

For Cylinder'

Formula to calculate the volume of cylinder is,

`V = \pi r^(2) h`..................................................(1)

where,

r - 2 inches

h - 3 inches

From the equation (1)

=
`\pi` ×
`2^(2)` × 3

= 37.70

V = 37.70 cubic inches

Step:2

For cone,

Formula to calculate the volume of cone is,

`V = \pi r^(2) (h)/(3)`..................................................(2)

From the statement,

cylinder and a cone have the same volume

`V_(cylinder)` =
`V_(cone)`

37.70 =
`\pi` ×
`3^(2)` ×
`(h)/(3)`

37.70 = 9.42478 × h

Height of the cone, h = 4 inches

Result:

Thus the height of the cone is 4 inches, if a cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.