The ratio of radii of two right circular cylinders (A and B) is 2:3. The ratio of volumes of the cylinders A and B is 9:7, then what is the ratio of the heights of the cylinders A and B?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 81:28
The volume of a cylinder is \(V=\pi r^2h\), so the ratio of two volumes is the ratio of the squares of the radii times the ratio of the heights. Knowing two of these ratios gives the third.
Ratio of the volumes: \(\displaystyle \frac{V_A}{V_B}=\frac{r_A^2}{r_B^2}\times\frac{h_A}{h_B}\)
The radii are in the ratio 2 : 3, so their squares are in the ratio 4 : 9; with the volume ratio 9 : 7, \(\displaystyle \frac{9}{7}=\frac{4}{9}\times\frac{h_A}{h_B}\)
\(\displaystyle \frac{h_A}{h_B}=\frac{9}{7}\times\frac{9}{4}=\frac{81}{28}\)