The radius of the base and height of a cone are 5 cm and 6 cm , respectively, whereas the radius of the base and height of a cylinder are 2.5 cm and 3 cm , respectively. The ratio of the volume of the cone to that of the cylinder is:
(Where π = $$\frac{22}7$$​)

Correct option is D

Given:
Radius of the base of the cone $$r_1 = 5 \, cm$$​​
Height of the cone $$h_1 = 6 \, {cm}$$​​
Radius of the base of the cylinder $$r_2 = 2.5 \, cm$$​​
Height of the cylinder $$h_2 = 3 \, cm$$​​
​$$\pi = \frac{22}{7}$$​

Formula Used:

​$$V_{\text{cone}} = \frac{1}{3} \pi r_1^2 h_1$$​​
​$$V_{\text{cylinder}} = \pi r_2^2 h_2$$​

Solution:

Volume of the cone:

​$$V_{\text{cone}} = \frac{1}{3} \times \frac{22}{7} \times (5^2) \times 6$$​

​$$V_{\text{cone}} = \frac{1}{3} \times \frac{22}{7} \times 25 \times 6$$​

​$$V_{\text{cone}} = \frac{1}{3} \times \frac{22}{7} \times 150$$​

​$$V_{\text{cone}} = \frac{3300}{21} = 157.14 \, \text{cm}^3$$​

Volume of the cylinder:

​$$V_{\text{cylinder}} = \frac{22}{7} \times (2.5^2) \times 3$$​

​$$V_{\text{cylinder}} = \frac{22}{7} \times 6.25 \times 3$$​

​Ratio of the volumes:

Ratio = $$\frac{V_{\text{cone}}}{V_{\text{cylinder}}} = \frac{\frac{1}{3} \times \frac{22}{7} \times 150}{\frac{22}{7} \times 6.25 \times 3} = \frac{8}{3}$$ 

Ratio = 8 : 3

The ratio of the volume of the cone to that of the cylinder is 8 : 3

Thus, the correct option is (d) 8 : 3