Question

A cylinder and the Sphere below have the same radius and the same volume. What is the height of the cylinder

Answer 1

The height of the cylinder is 8m.

Explanation:

Given, the Radius and Volume of the cylinder and sphere are equal.

Radius, r = 6m

Formula,

Volume of the sphere =
`(4)/(3)\pi r^(3)`

Volume of the cylinder =
`\pi r^(2)h`

⇒ Volume of the cyliner = Volume of Sphere

⇒
`(4)/(3)\pi r^(3)` = 
`\pi r^(2)h`

⇒
`h = (4\pi r^(3) )/(3\pi r^(2) )`

⇒
`h = (4r)/(3)`

⇒
`h = (4 * 6)/(3)`

⇒ h = 8m

Answer 2

8 m

Explanation:

Volume of a sphere is V = 4/3 π r³.

Volume of a cylinder is V = π r² h.

The two volumes are equal, so:

4/3 π r³ = π r² h

4/3 r = h

The radius is 6 m, so the height of the cylinder is:

h = 4/3 (6 m)

h = 8 m