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. 10:17
• B. 20:27
• C. 17:27
• D. 20:37

Hint:

For volume problems involving ratios of radii and heights, use the formula for the volume of a cylinder and apply the ratios to find the answer.

Answer 1

The Correct Option is B

The formula for the volume of a cylinder is \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. 
Step 1: Let the radii of the two cylinders be \( r_1 \) and \( r_2 \), and the heights be \( h_1 \) and \( h_2 \). \[ \frac{r_1}{r_2} = \frac{2}{3}, \quad \frac{h_1}{h_2} = \frac{5}{3} \] 
Step 2: The ratio of their volumes is: \[ \frac{V_1}{V_2} = \frac{r_1^2 h_1}{r_2^2 h_2} \] \[ \frac{V_1}{V_2} = \frac{\left(\frac{2}{3}\right)^2 \times \frac{5}{3}}{1} = \frac{4}{9} \times \frac{5}{3} = \frac{20}{27} \] Thus, the ratio of their volumes is 20:27.