Question

Cylinder A has a radius of 12 inches and a height of 6 inches. Cylinder B has a volume of 648(pi). What is the percent change in volume between cylinders A and B?

Answer 1

`\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=12\\ h=6 \end{cases}\implies V=\pi (12)^2(6)\implies \stackrel{\textit{volume of A}}{V=864\pi }`

so their difference is 864π - 648π = 216π.

if we take 864π to be the 100%, what is 216π off of it in percentage?

`\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 864\pi &100\\ 216\pi &x \end{array}\implies \cfrac{864\pi }{216\pi }=\cfrac{100}{x}\implies 4=\cfrac{100}{x} \\\\\\ 4x=100\implies x=\cfrac{100}{4}\implies x=25`