Respuesta :
the surface area of the sphere is π/4 cm^3
How to determine the surface area
It is important to know the formula for surface area and volume of a sphere
Surface area = [tex]\frac{4\pi }{r^2}[/tex]
Volume = [tex]\frac{4}{3} \pi r^3[/tex]
First, let's determine the value of radius, r
The value for volume was given as 256/3π cm3.
[tex]\frac{256}{3} \pi = \frac{4}{3} \pi r^3[/tex]
Pi cancels out and we have cross multiply to get the radius
[tex]256 * 3 = 4 * 3 r^3[/tex]
[tex]12r^3 = 768[/tex]
Make r the subject of the formula
[tex]r = \sqrt[3]{\frac{768}{12} }[/tex]
[tex]r = \sqrt[3]{64}[/tex]
r = 4
Let's substitute to find the surface area
Surface area = [tex]\frac{4\pi }{4^2}[/tex]
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:
https://brainly.com/question/10171109
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