Question

The measures of a sphere with a volume of 972pi in^3 are multiplied by 1/3.

What is the volume of the sphere?

A) 324pi in^3
B) 108pi in^3
C) 54pi in^3
D 36pi in^3

Answer 1

`\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \boxed{r=(1)/(3)r}\qquad V=\cfrac{4\pi }{3}\left( \cfrac{r}{3} \right)^3\implies V=\cfrac{4\pi }{3}\cdot \cfrac{r^3}{3^3} \\\\\\ V=\cfrac{4\pi r^3}{3}\cdot \cfrac{1}{3^3}\implies V=\cfrac{4\pi r^3}{3}\cdot \cfrac{1}{27}\impliedby (1)/(27)\textit{ of the original volume} \\\\\\ \textit{what is }(1)/(27)\textit{ of }972\pi ?\qquad \qquad 972\pi \cdot \cfrac{1}{27}\implies 36\pi`