Surface Area of Sphere with volume 2048/3(pi)

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If the volume of a sphere is 2048/3[pi], find its surface area. I got 803.84, but the textbook reveals another answer as correct.

What I did:

4/3[pi]r^3 = 2048/3[pi]
x3 = x3
/[pi] = /[pi]

Now I have:

4r^3 = 2048
/4 = /4

Now I have:

r^3 = 512

I found the third root of 512, and got 8. So, I plugged 8 into the
formula for surface area:

SA = 4[pi]r^2 = 4 x 3.14 x 8^2

My answer was 803.84!!! Am I wrong? If so, please tell me what I did
wrong.

Should the answer be 256pi = SA?
 
I guess you mean:

\(\displaystyle \L\\\frac{4}{3}{\pi}r^{3}=\frac{2048\pi}{3}\)

You have \(\displaystyle \L\\\frac{2048}{3\pi}\) in your post. Different animal.

Please be sure you use parentheses as not to be too confusing.

Assuming you mean the former, \(\displaystyle \L\\256{\pi}\approx{804.25}\) is, indeed, the correst answer.
 
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