Question

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

Answer 1

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