Question

The base radii of two right circular cones of the same height are in the ratio 3 : 5.

Assertion (A): The ratio between their volumes is 9 : 25.

Reason (R): As \[\frac{r_{1}}{r_{2}}=\frac{3}{5}\]

\[ \frac{\pi r_{1}^{2} h}{\pi r_{2}^{2} h}=\frac{r_{1}^{2}}{r_{2}^{2}}=\left(\frac{3}{5}\right)^{2}\]

विकल्प

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Given, the base radius of two right circular cone of the same height are in ratio 3 : 5.

As we know that volume of cone \[= \frac{1}{3}\, \pi r^2 h\]

\[\frac{\text{Volume of 1st cone}}{\text{Volume of 2nd cone}} = \frac{\frac{1}{3}\, \pi r_1^2 h}{\frac{1}{3}\, \pi r_2^2 h}\]

\[{} = \frac{\pi r_1^2 h}{\pi r_2^2 h}\]

\[{} = \frac{r_1^2}{r_2^2}\]

\[{} = \frac{3^2}{5^2}\]

\[{} = \left(\frac{3}{5}\right)^2\]

\[{} = \frac{9}{25}\]

∴ Both A and R are true and R is correct reason for A.