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

For the first part it would be 38772.72 cm^3 and for the second part it would be 65 minutes to fill the container.

Answer 2

The volume of the container is
`38,772.72\ cm^(3)`

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

we have

`r=21\ cm`

`\pi=3.14`

substitute the values

`V=(4)/(3)(3.14)(21)^(3)=38,772.72\ cm^(3)`