Question

A cylinder and a sphere have the same radius. The height of the cylinder is three times its radius. Then the ratio of the volume of the cylinder to the volume of the sphere is:

• A. 1 : 3
• B. 3 : 1
• C. 9 : 4
• D. 4 : 9

Hint:

Cancel common terms like $\pi r^3$ to simplify volume ratios quickly.

Answer 1

The Correct Option is C

Concept: Use formulas: \[ V_{{cylinder}} = \pi r^2 h,\quad V_{{sphere}} = \frac{4}{3}\pi r^3 \]
Step 1: Given $h = 3r$.
\[ V_{{cylinder}} = \pi r^2 (3r) = 3\pi r^3 \]
Step 2: Volume of sphere.
\[ V_{{sphere}} = \frac{4}{3}\pi r^3 \]
Step 3: Find ratio.
\[ \frac{3\pi r^3}{\frac{4}{3}\pi r^3} = \frac{3}{4/3} = \frac{9}{4} \]
Hence, the ratio is $9:4$.