Discussion
Water is flowing at the rate of 10 km/hr through a cylindrical pipe of diameter 14 cm into a rectangular tank which is 100 m long and 44 m wide. In what time the level of water in the tank will be risen by 7 cm ?
Answer: C
The level rises by 7 cm in 2 hours.
The volume needed is the tank's base area times the rise in level, 7 cm or 0.07 m:
\[ 100 \times 44 \times 0.07 = 308\ \text{m}^{3} \]
The pipe has radius 7 cm, 0.07 m, and water moves 10 km, 10 000 m, in an hour, so the flow per hour is:
\[ \begin{aligned} \pi r^{2} \times 10000 &= \tfrac{22}{7} \times 0.0049 \times 10000 \\ &= 154\ \text{m}^{3} \end{aligned} \]
Time = \(308 \div 154 = 2\) hours. Using the diameter instead of the radius would give a flow four times larger and a time of half an hour.
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