Question

The surface area of a sphere is 275.56 1 cm? What is the approximate volume of the sphere?

A. 2,287.15 pi cm3
B. 762.38 pi cm3
C. 6,099.06 pi cm3
D. 381.19cm3

Answer 1

`V=430.19\ cm^3` or
`V=136.93\pi\ cm^3`

Explanation:

The surface area of a sphere is:

`A_s=4\pi r^2`

Where r is the radius of the sphere

In this case we know that
`A_s = 275.561\ cm^2`

So

`4\pi r^2=275.561`

We solve the equation for r

`4\pi r^2=275.561\\r^2 = (275.561)/(4\pi)\\\\r=\sqrt{ (275.561)/(4\pi)}\\\\r=4.683\ cm`

Now we know the radius of the sphere.

The volume of a sphere is:

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

We substitute the value of the radius in the formula

`V=(4)/(3)\pi (4.683)^3`

`V=430.19\ cm^3`