Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 120 cubic inches. A sphere with height h and radius r. A cylinder with height h and radius r. What is the volume of the sphere? A.40 cubic inches B 90 cubic inches. C 160 cubic inches D 360 cubic inches

Answer 1

Option C. 160
`inch^(3)` is the correct answer.

Explanation:

We are given that height and radius of sphere and cylinder are same.

Radius 'r' and height 'h'.

We know that Volume of cylinder =
`\pi r^(2) h`

Also, h = r,

So, volume of cylinder =
`\pi r^(3) = 120\ inch^(3) ...... (1)`

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

Using equation (1), putting the value of
`\pi r^(3)`

`\Rightarrow (4)/(3) * 120\\\Rightarrow 160\ inch^(3)`

Hence, volume is sphere is option 3)
`160\ inch^(3)`