the surface area of the sphere is π/4 cm^3
<h3>How to determine the surface area</h3>
It is important to know the formula for surface area and volume of a sphere
Surface area = ![\frac{4\pi }{r^2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cpi%20%7D%7Br%5E2%7D)
Volume = ![\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
First, let's determine the value of radius, r
The value for volume was given as 256/3π cm3.
![\frac{256}{3} \pi = \frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=%5Cfrac%7B256%7D%7B3%7D%20%5Cpi%20%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
Pi cancels out and we have cross multiply to get the radius
![256 * 3 = 4 * 3 r^3](https://tex.z-dn.net/?f=256%20%2A%203%20%3D%204%20%2A%203%20r%5E3)
![12r^3 = 768](https://tex.z-dn.net/?f=12r%5E3%20%3D%20768)
Make r the subject of the formula
![r = \sqrt[3]{\frac{768}{12} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B768%7D%7B12%7D%20%7D)
![r = \sqrt[3]{64}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B64%7D)
r = 4
Let's substitute to find the surface area
Surface area = ![\frac{4\pi }{4^2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cpi%20%7D%7B4%5E2%7D)
Surface area = π/4
Surface area = π/4 cm^3
Thus, the surface area of the sphere is π/4 cm^3
Learn more about a sphere here:
brainly.com/question/10171109
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