Question

The volume of a sphere is 5,000pi m3. What is the surface area of the sphere to the nearest square meter?

Answer 1

Answer: $1024\pi\ m^2$

Step-by-step explanation:

The volume of a sphere is given by :-

$\text{Volume}=\dfrac{4}{3}\pi\ r^3$, where r is the radius of the sphere.

Given: The volume of a sphere =$5,000\pi\ m^3$

$\Rightarrow5000\pi=\dfrac{4}{3}\pi r^3\\\\\Rightarrow\ r^3=\dfrac{3}{4}\times5000\\\\\Rightarrow\ r^3=3750\\\\\Rightarrow\ r=15.536162\approx16\ m$

The surface area of sphere is given by :-

$\text{SA}=4\pi r^2\\\\\Rightarrow\text{SA}=4\pi(16)^2\\\\\Rightarrow\ SA=1024\pi\ m^2$

Answer 2

Surface area of a sphere = 4πr2
 the volume of a sphere= 43πr3
 so 5000π=4/3πr3
> r^3 = 5000 x 3 / 4 =>
 r^3 = 3750
taking cube root on both sides
r=15.53616
hope it helps