How much time to fill?

Geometry Level 3

A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at a rate of 2 metres per sec. In how much time will tank be filled (in minutes)?

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The answer is 28.

Vignesh Rao by Vignesh Rao , 20, India

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2 solutions

Vignesh Rao
Dec 23, 2015

Volume of cylindrical tank = π r 2 h = ( π × 70 × 70 × 210 ) cm 3 \pi r^2 h = ( \pi \times 70 \times 70 \times 210) \text{ cm}^3 ...(i)

Volume of water added in each second = Area of cross section of pipe × Rate of water flow \text{Area of cross section of pipe} \times \text{Rate of water flow}

⇒ ( π × 3.5 2 × 3.5 2 ) cm 2 × ( 200 ) cm/sec \Rightarrow (\pi \times \frac{3.5}{2} \times \frac{3.5}{2})\text{ cm}^2 \times (200)\text{ cm/sec} ...(ii)

Time taken to fill = Eqn. (i) Eqn. (ii) ⇒ ( π × 70 × 70 × 210 ) ( π × 3.5 2 × 3.5 2 × 200 ) = 1680 seconds = 28 minutes \frac{\text{Eqn. (i)}}{\text{Eqn. (ii)}}\\ \Rightarrow \frac{( \pi \times 70 \times 70 \times 210)}{(\pi \times \frac{3.5}{2} \times \frac{3.5}{2}\times 200)} = 1680 \text{ seconds} = 28 \text{ minutes}

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time = volume volume flow rate = π 4 ( 1.4 ) 2 ( 2.1 ) π 4 ( 0.035 ) 2 ( 2 ) = 1680 seconds \text{time}=\dfrac{\text{volume}}{\text{volume flow rate}}=\dfrac{\dfrac{\pi}{4}(1.4)^2(2.1)}{\dfrac{\pi}{4}(0.035)^2(2)}=1680~\text{seconds}

But in 1 1 minute, there are 60 60 seconds, so the desired answer is 28 minutes 28~\text{minutes} .

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