Question

Cylinder A has twice the radius and three times the height of cylinder B. What is the ratio of the volume of cylinder A to the volume of cylinder B?

Answer 1

`6:1`

Explanation:

`\mathrm{Solution:}\\\mathrm{Let:}\\\mathrm{For\ cylinder\ A:}\\\mathrm{Height=h_A\ and\ radius=r_A}\\\mathrm{For\ cylinder\ B:}\\\mathrm{Height=h_B\ and\ radius=r_B}\\\mathrm{Given:\ r_A=2r_B,\ h_A=3h_B}\\`

`\mathrm{Now,}\\\mathrm{Volume\ of\ cylinder\ A(V_A)=\pi (r_A)^2h_A=\pi (2r_B)^2(3h_B)=6\pi (r_B)^2h_B}\\\mathrm{Volume\ of\ cylinder\ B(V_B)=\pi (r_B)^2h_B}\\\mathrm{Finally,}\\\mathrm{Ratio=(V_A)/(V_B)=(6\pi (r_B)^2h_B)/(\pi (r_B)^2h_B)=(6)/(1)=6:1}`