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Water is flowing at the rate of 15 km/hr through a cylindrical pipe with a diameter of 14 cm into a cuboidal pond that is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?

(a) 9 hours
(b) 12 hours
(c) 15 hours
(d) 18 hours

Answer :

Final answer:

The water level in the pond will rise by 21 cm in 12 hours.

Thus, the correct option is b.

Explanation:

To find the time it takes for the water level to rise by 21 cm in the cuboidal pond, we need to calculate the volume of water flowing through the pipe per unit time and then relate it to the increase in volume of the pond.

First, we find the cross-sectional area of the pipe using its diameter:

[tex]\[ \text{Area} = \pi \times \left(\frac{14}{2}\right)^2 = 154 \, \text{cm}^2 \][/tex]

Next, we convert the water flow rate from km/hr to cm/hr:

[tex]\[ 15 \, \text{km/hr} = 15,000 \, \text{m/hr} = 15,000,000 \, \text{cm/hr} \][/tex]

Then, we find the volume of water flowing per hour:

[tex]\[ \text{Volume} = \text{Area} \times \text{speed} = 154 \times 15,000,000 = 2,310,000,000 \, \text{cm}^3/\text{hr} \][/tex]

Finally, we find the time required to raise the water level in the pond:

[tex]\[ \text{Time} = \frac{\text{Volume of rise}}{\text{Volume flow rate}} = \frac{50 \times 44 \times 21}{2,310,000,000} = \frac{46200}{231000000} \, \text{hours} \][/tex]

[tex]\[ = \frac{77}{385} \, \text{hours} \][/tex]

[tex]\[ = \frac{1}{5} \, \text{hours} \][/tex]

[tex]\[ = 12 \, \text{hours} \][/tex]

Therefore, the correct answer is (b) 12 hours.

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