Question

The volume of a sphere is 256/3π cm3.

Answer 1

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 = $\frac{4\pi }{r^2}$

Volume = $\frac{4}{3} \pi r^3$

First, let's determine the value of radius, r

The value for volume was given as  256/3π cm3.

$\frac{256}{3} \pi = \frac{4}{3} \pi r^3$

Pi cancels out and we have cross multiply to get the radius

$256 * 3 = 4 * 3 r^3$

$12r^3 = 768$

Make r the subject of the formula

$r = \sqrt[3]{\frac{768}{12} }$

$r = \sqrt[3]{64}$

r = 4

Let's substitute to find the surface area

Surface area = $\frac{4\pi }{4^2}$

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

#SPJ1