Question

Find the surface area of a sphere with a volume of 36π in^3.

Answer 1

To find the surface area of a sphere, you want to use the formula:
4π r^2
We are given with the volume of a sphere. The volume of the sphere is:
36π
We need to find the radius of the sphere to get the surface area, correct?

Answer 2

yes

Answer 3

Oh yeah, to find the volume of a sphere, you use the formula:
(4/3) π r^3
So:
(4/3) π r^3 = 30π
We want to find r. So what do we do first?

Answer 4

cancel out pi on both sides

Answer 5

Alright. So we would get:
(4/3) r^3 = 30

Now what would we do?

Answer 6

divide both sides by 4/3?

Answer 7

Hmm. We want to get rid of (4/3).
So (4/3) divided by (4/3) cancel out?

Answer 8

yup

Answer 9

Okay. So what does 30 divided by (4/3) give you?

Answer 10

22.5

Answer 11

Hmm. Alright.
So we have:
r^3 = 22.5
Now what would we do?

Answer 12

this is the part i dont get. if it was r^2 you would just find the square root of 22.5 but i dont know how to do it with r^3

Answer 13

Well. If you want to get rid of square, then you would square root it.
If you want to get rid of cube, then you would have to cube root it.

Answer 14

so how do you do that

Answer 15

It would look like: \[\large \large \large \sqrt[3]{22.5}\] You can use a calculator if you want.

Answer 16

so the answer is about 2.82

Answer 17

Yes. Correct. So the radius is 2.82, approximately. Now to find the surface area of the sphere, you use the formula: 4π r^2

All you need to do is plug it in.
After plugging it in, your equation should look like:

4π * 2.82^2

Answer 18

oh okay that makes sense! thank you!

Answer 19

No problem. :)
I hope this help!