Question

A sphere has a volume of 500/3 π cubic centimeters. What is the total surface area , in square centimeters, of the sphere

Answer 1

`\large\boxed{S.A.=100\pi\ cm^3\approx314\pi\ cm^2}`

Explanation:

The formula of a volume of a sphere:

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

R - radius

We have

`V=(500)/(3)\pi\ cm^3`

Substitute and solve for R:

`(500)/(3)\pi=(4)/(3)\pi R^3` divide both sides by π

`(500)/(3)=(4)/(3)R^3` multiply both sides by 3

`500=4R^3` divide both sides by 4

`125=R^3\to R=\sqrt[3]{125}\\\\R=5\ cm`

The formula of a Surface Area os a sphere:

`S.A.=4\pi R^2`

Substitute:

`S.A.=4\pi(5^2)=4\pi(25)=100\pi\ cm^2`

`\pi\apprx3.14\to S.A.\approx(100)(3.14)=314\ cm^2`