Question

Please help me with this

Answer 1

`(4000\pi)/(3)` ft³

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
`A = 4\pi r^2`

The formula for a sphere's volume is
`V=(4)/(3)\pi r^3`

So to get from area to volume, we have to divide the area by 3 and then multiply it by r. Mathematically:

`V=(A)/(3)r`

Before we solve for V though, we need to find the radius of our sphere. Thankfully, we're given the surface area -
`400\pi` ft² - so we can use the area formula to find that radius:

`A=4\pi r^2=400\pi\\r^2=100\\r=10`

And now that we have our radius, we can put it into our volume formula to find

`V=(A)/(3) r=(400\pi)/(3)(10)=(4000\pi)/(3)` ft³