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`

Explanation:

The volume of a sphere is given by :-

`\text{Volume}=(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=(4)/(3)\pi r^3\\\\\Rightarrow\ r^3=(3)/(4)*5000\\\\\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