Question

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

• A. \(27:20\)
• B. \(20:27\)
• C. \(4:9\)
• D. \(9:4\)

Hint:

For similar solids where \(V\propto r^2h\) (cylinders), square the radius ratio and multiply by the height ratio to get the volume ratio.

Answer 1

The Correct Option is B

Step 1: Recall the volume formula of a cylinder.
\(V=\pi r^2 h\). For two cylinders, \(V_1:V_2=(r_1^2 h_1):(r_2^2 h_2)\).
Step 2: Substitute the given ratios.
\(r_1:r_2=2:3 \Rightarrow r_1^2:r_2^2=4:9\).
\(h_1:h_2=5:3\).
Step 3: Multiply component-wise.
\[ V_1:V_2=(4\times 5):(9\times 3)=20:27. \]