Question

The volume of a cylinder with height to radius ratio of 4:1 is 108 pie centimeters cubed. Find the radius and height of the cylinder.

Answer 1

$H:r=4:1\\\\\frac{H}{r}=\frac{4}{1}\to H=4r\ (*)\\\\V=108\pi\ cm^3\\\\V=\pi r^2H\\\\substitute\ (*)\\\\\pi r^2\cdot4r=108\pi\ \ \ \ /:4\pi\\\\r^3=27\\\\r=\sqrt[3]{27}\\\\r=3\ (cm)\\\\H=4r=4\cdot3=12\ (cm)\\\\Answer:radius=3\ cm\ and\ height=12\ cm.$

Answer 2

4:1 height to radius
let x be radius
let 4x be height

V=(pi)(r)^2h
108(pi)=(pi)x^2(4x)
divide both sides by pi
108=x^2(4x)
108=4x^3
divide both sides by 4
27=x^3
cube root both sides
x=3

therefore the radius is 3 and the height is 12