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:

For similar cylinders, the volume ratio is: \[ \frac{V_1}{V_2} = \frac{r_1^2 h_1}{r_2^2 h_2} \]

Answer 1

The Correct Option is A

The volume of a cylinder is:
\[ V = \pi r^2 h \] Let the radii be \( 2x \) and \( 3x \), and the heights be \( 5y \) and \( 3y \).
\[ \frac{V_1}{V_2} = \frac{\pi (2x)^2 (5y)}{\pi (3x)^2 (3y)} \] \[ = \frac{4x^2 \cdot 5y}{9x^2 \cdot 3y} = \frac{20}{27} \]