Question

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

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

Hint:

When comparing the volumes of similar shapes, always apply the correct power for each dimension: squared for area and cubed for volume.

Answer 1

The Correct Option is B

Step 1: Formula for volume of a cylinder
The volume \( V \) of a cylinder is given by: \[ V = \pi r^2 h \] Step 2: Substituting given ratios
Let the radii be \( 2x \) and \( 3x \), and the heights be \( 5y \) and \( 3y \).
Volume of first cylinder: \[ V_1 = \pi (2x)^2 (5y) = \pi (4x^2)(5y) = 20\pi x^2 y \] Volume of second cylinder: \[ V_2 = \pi (3x)^2 (3y) = \pi (9x^2)(3y) = 27\pi x^2 y \] Step 3: Ratio of volumes
\[ V_1:V_2 = 20:27 \] Thus, the correct answer is 20:27.