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

Answer:

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

Step-by-step 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

$4\pi r^2=275.561\\r^2 = \frac{275.561}{4\pi}\\\\r=\sqrt{ \frac{275.561}{4\pi}}\\\\r=4.683\ cm$

Now we know the radius of the sphere.

The volume of a sphere is:

$V=\frac{4}{3}\pi r^3$

We substitute the value of the radius in the formula

$V=\frac{4}{3}\pi (4.683)^3$

$V=430.19\ cm^3$