Question

a spherical container has surface area of about 5,538.96 square centimeters. what is the volume lf the container? use 3.14 for pi, and round to the nearest hundredth

Answer 1

Answer:

The volume of the container is $38,772.72\ cm^{3}$

Step-by-step explanation:

step 1

Find the radius of the sphere

we know that

The surface area of a sphere is equal to

$SA=4\pi r^{2}$

we have

$SA=5,538.96\ cm^{2}$

$\pi=3.14$

substitute the values and solve for r

$5,538.96=4(3.14)r^{2}$

$r^{2}=5,538.96/[4(3.14)]$

$r^{2}=441$

$r=21\ cm$

step 2

Find the volume of the container

The volume of the sphere (container) is equal to

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

we have

$r=21\ cm$

$\pi=3.14$

substitute the values

$V=\frac{4}{3}(3.14)(21)^{3}=38,772.72\ cm^{3}$