Answer:
[tex]\dfrac{4000\pi}{3}[/tex] ft³
Step-by-step explanation:
First, let's figure out how to get the volume of a sphere from its surface area. If r is the radius of our sphere, then
The formula for a sphere's surface area is [tex]A = 4\pi r^2[/tex]
The formula for a sphere's volume is [tex]V=\frac{4}{3}\pi r^3[/tex]
So to get from area to volume, we have to divide the area by 3 and then multiply it by r. Mathematically:
[tex]V=\frac{A}{3}r[/tex]
Before we solve for V though, we need to find the radius of our sphere. Thankfully, we're given the surface area - [tex]400\pi[/tex] ft² - so we can use the area formula to find that radius:
[tex]A=4\pi r^2=400\pi\\r^2=100\\r=10[/tex]
And now that we have our radius, we can put it into our volume formula to find
[tex]V=\frac{A}{3} r=\frac{400\pi}{3}(10)=\frac{4000\pi}{3}[/tex] ft³
