Question

PLEASE SOMEONE ANSWER THIS FOR ME

Identify the volume and surface area of a sphere with great circle area 144π ft2 in terms of π.

Answer 1

check the picture below.


`\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=144\pi \end{cases}\implies 144\pi =\pi r^2 \\\\\\ \cfrac{144\pi }{\pi }=r^2\implies 144=r^2\implies √(144)=r\implies \boxed{12=r}\\\\ -------------------------------`


`\bf \textit{since the sphere then, has a \underline{radius of 12}} \\\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \implies V=\cfrac{4\pi (12)^3}{3}\implies V=2304\pi \\\\\\ \textit{surface area of a sphere}\\\\ SA=4\pi r^2\qquad \implies SA=4\pi (12)^2\implies SA=576\pi`