Question

The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is

• A. 27 : 20
• B. 20 : 27
• C. 4 : 9
• D. 9 : 40

Hint:

The volume ratio of two cylinders is the square of the ratio of their radii times the ratio of their heights.

Answer 1

The Correct Option is A

The volume of a cylinder is given by: \[ V = \pi r^2 h, \] where \( r \) is the radius and \( h \) is the height. The ratio of volumes of the two cylinders is: \[ \frac{V_1}{V_2} = \frac{r_1^2 h_1}{r_2^2 h_2}. \] Given \( \frac{r_1}{r_2} = \frac{2}{3} \) and \( \frac{h_1}{h_2} = \frac{5}{3} \), the ratio of volumes becomes: \[ \frac{V_1}{V_2} = \left(\frac{2}{3}\right)^2 \times \frac{5}{3} = \frac{4}{9} \times \frac{5}{3} = \frac{20}{27}. \] Thus, the correct answer is \( 27 : 20 \).