Question

A sphere has a volume of V=324 in^3. Find it's surface area ​

Answer 1

The surface area of the sphere is
`108\pi \sqrt[3]{3}\ in^(2)`

Explanation:

In this problem the volume should be
`V=324\pi \ in^(3)` instead of
`V=324\ in^(3)`

step 1

Find the radius of the sphere

The volume of the sphere is equal to

`V=(4)/(3)\pi r^(3)`

we have

`V=324\pi \ in^(3)`

substitute and solve for r

`324\pi=(4)/(3)\pi r^(3)`

simplify

`r^(3)=324*3/4`

`r=\sqrt[3]{243}\ in`

step 2

Find the surface area of the sphere

The surface area of the sphere is equal to

`SA=4\pi r^(2)`

we have

`r=\sqrt[3]{243}\ in`

substitute

`SA=4\pi(\sqrt[3]{243})^(2)`

simplify

Remember that

`(\sqrt[3]{243})^(2)=243^((2/3)) =27\sqrt[3]{3}`

`SA=4\pi(27\sqrt[3]{3})=108\pi \sqrt[3]{3}\ in^(2)`