Question

The dimensions of the smaller cylinder are two-thirds of the dimensions of the larger cylinder. The volume of the larger cylinder is 2160 pi cm3. Find the volume of the smaller cylinder.

Answer 1

If r is the radius and h is the height of the smaller cylinder, then the radius and height of the smaller cylinder is given by (2/3)r and (2/3)h. The volume of the larger cylinder is given by\[V_L=\pi r^2h=2160 \pi\]The volume of the smaller cylinder is given by\[V_S=\pi \left( \frac23 r \right)^2\left( \frac23h \right)= \left( \frac23 \right)^3\pi r^2h=\left( \frac23 \right)^3V_L\]