Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 cm

What is the volume of the sphere?
O 12 cm
O 24 cm
O 36 cm
54 cm

Answer 1

We have been given that a sphere and a cylinder have the same radius and height.

We know that height of sphere is equal to its radius. So
`h=r`.

Now we will use volume of sphere and volume of cylinder formula to solve our given problem.

Volume of cylinder:
`V=\pi r^2h`, where,

r = Radius,

h = Height

Volume of sphere:
`V=(4)/(3)\pi r^3`, where,

r = Radius.

Since height is equal to radius, so we will get:

`V=\pi r^2\cdot r=\pi r^3`

Since volume of cylinder is
`18` cubic cm, so we will equate volume formula with
`18` as:

`\pi r^3=18`

Let us solve for r.

`(\pi r^3)/(\pi)=(18)/(\pi)`

`r^3=(18)/(\pi)`

`r=\sqrt[3]{(18)/(\pi)}`

Upon substituting this value in volume of sphere formula, we will get:

`V=(4)/(3)\pi\cdot \left(\sqrt[3]{(18)/(\pi)}\right)^3`

`V=(4)/(3)\pi\cdot (18)/(\pi)`

`V=(4)/(1)\cdot 6`

`V=24`

Therefore, the volume of the sphere would be 24 cubic cm and option B is the correct choice.