Geometry

Solids

Medium

Water flows at the rate of $5$ km/hr through a pipe of diameter $14$ cm into a rectangular tank that is $50$ m long and $44$ m wide. Determine the time in which the level of the water in the tank will rise by $7$ cm.

(Assume $\pi = 22/7$ )

0.5 hrs

1 hr

2 hrs

None of these

✅ Correct Option: 3

Pipe diameter = $14$ cm, so radius = $\dfrac{14}{2} = 7$ cm

Area of circular pipe = $\pi r^2$

$= \dfrac{22}{7} \times 7^2$

$= \dfrac{22}{7} \times 49$

$= 22 \times 7$

$= 154$ cm²

Water speed = $5$ km/hr

$= 5 \times 1000 \times 100$

$= 500,000$ cm/hr

Volume flow rate = Area × Speed

$= 154 \times 500,000$

$= 77,000,000$ cm³/hr

Tank dimensions:

Length = $50$ m = $5000$ cm

Width = $44$ m = $4400$ cm

Height rise needed = $7$ cm

Volume needed = $5000 \times 4400 \times 7$

$= 154,000,000$ cm³

Time = $\dfrac{\text{Volume needed}}{\text{Volume flow rate}}$

$= \dfrac{154,000,000}{77,000,000}$

$= \dfrac{154}{77}$

$= 2$ hours

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BMSAT Kozhikode Past Year Questions (Topic-Wise)

Water flows at the rate of $5$ km/hr through a pipe of diameter $14$ cm into a rectangular tank that is $50$ m long and $44$ m wide. Determine the time in which the level of the water in the tank will rise by $7$ cm.

(Assume $\pi = 22/7$ )