Question

Find the volume (in terms of pi) of a sphere of its surface area is 400 pi ft2

Answer 1

$\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2\qquad \qquad \implies \stackrel{SA}{400\pi }=4\pi r^2\implies \cfrac{400\pi }{4\pi }=r^2 \\\\\\ 100=r^2\implies \sqrt{100}=r\implies \boxed{10=r} \\\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad V=\cfrac{4\pi \boxed{10^3}}{3}\implies V=\cfrac{4000\pi }{3}$

Answer 2

Answer: $1333.33\pi\ ft.^3$

Step-by-step explanation:

The surface area of sphere is given by :-

$S.A=4\pi r^2$, where r is radius of sphere.

Given : Surface area of sphere =$400 \pi \ft2$

$\\\Rightarrow 400 \pi =4\pi r^2\\\\\Rightarrow\ r^2=\dfrac{400}{4}=100\text{ ft.}$

The volume of sphere is given by :-

$V=\dfrac{4}{3}\pi r^3\\\\\Rightarrow\ V=\dfrac{4}{3}\pi (100)^3\\\\\Rightarrow\ V=\dfrac{4000}{3}\pi=1333.33333\approx1333.33\pi\ ft.^3$