Question

A cylinder has a volume of 360 in^3. If the height and radius are multiplied by 2.5, what will the resulting volume be?

A) 5525 in^3
B) 2880 in^3
C) 5400 in^3
D) 3600 in^3

Answer 1

`\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=2.5r\\ h=2.5h \end{cases}\implies V=\pi (2.5r)^2(2.5h) \\\\\\ V=\pi \cdot 2.5^2\cdot r^2\cdot 2.5h\implies V=(2.5^2\cdot 2.5)\pi r^2 h \\\\\\ V=15.625\pi r^2h\impliedby \textit{15.625 of the original} \\\\\\ \textit{if the original was 360}\qquad 15.265\cdot 360`