Question

a cylinder and a cone have the same volume. The cylinder has a radius of 2inches and a height of 3 inches. the cone has a radius of 3 inches. what is the height of the cone? show work.

Answer 1

Volume of a cone and cylinder

The height of the cone is 4 inches

Explanation:

The volume of cylinder =
`\pi * r^(2) * h\\`

The volume of cone =
`1/3 * \pi * r^(2) * h\\`

Value of
`\pi`= 3.14

In case of cylinder the value of radius r = 2 inches and height = 3 inches

Therefore, the volume of the cylinder is given by:

V1 =
`\pi * r^(2) * h\\` = ---------------------------( 1 )

⇒ V1= 3.14 ×2 ×2 ×3

⇒V1 = 3.14 ×12

⇒V1 =37.68 cubic inch

Volume of cone V2 =
`1/3 * \pi * r^(2) * h\\` --------------------------------------( 2)

V2 = 1/3 ×3.14 ×3 ×3 ×h as r =3 inches

Also, given that the volume of cylinder V1 is equal to volume of cone V2 V1 = V2

So equating equation (1) with equation (2 )

So

1/3 ×3.14 ×3 ×3 ×h = 37.68

⇒3.14 ×3 ×h = 37.68

⇒h = 37.68 / ( 3 × 3.14)

⇒ h = 4

Hence, the height of the cone is 4 inches