​Water flows through a pipe which is of cylindrical shape of radius 2.5 mm at rate of 10 m per minute and falls into a conical tub of 20 cm base radius and 24 cm height. How long will it take to fill the tub?​

Correct option is D

Given:
Cylindrical Pipe:

Radius  r  = 2.5 mm = 0.25 cm
Flow rate = 10 meters per minute = 1000 cm per minute
Conical Tub:
Base radius R  = 20 cm
Height H = 24 cm
Concept Used:
Volume of a cylinder:  $$V_{\text{cylinder}} = \pi r^2 h$$​​
Volume of a cone:  $$V_{\text{cone}} = \frac{1}{3} \pi R^2 H$$​​
Flow rate is the volume of water flowing per unit time.
Solution:
$$V_{\text{cone}} = \frac{1}{3} \pi R^2 H$$​

$$V_{\text{cone}} = \frac{1}{3} \pi (20)^2 (24)$$​​
$$V_{\text{cone}} = \frac{1}{3} \pi (400) (24)$$​​
$$V_{\text{cone}} = \frac{1}{3} \pi (9600)$$​​
$$V_{\text{cone}} = 3200 \pi \text{ cm}^3$$​
First, find the cross-sectional area of the pipe:
$$A = \pi r^2$$​​
$$A = \pi (0.25)^2$$​​
$$A = \pi (0.0625)$$​​
$$A = 0.0625 \pi \text{ cm}^2$$​​
Volume flow rate per minute:
$$V_{\text{flow}} = A \times \text{flow rate}$$​​
$$V_{\text{flow}} = 0.0625 \pi \times 1000$$​​
$$V_{\text{flow}} = 62.5 \pi \text{ cm}^3/\text{minute}$$​​
$$\text{Time} = \frac{V_{\text{cone}}}{V_{\text{flow}}}$$​​

$$\text{Time} = \frac{3200 \pi}{62.5 \pi}$$​

$$\text{Time} = \frac{3200}{62.5}$$​​
Time= 51.2 minutes= 51 minutes12 seconds