A cylindrical tank of radius $10 m$ is being filled with wheat at the rate of $314$ cubic metre per hour. then the depth of the wheat is increasing at the rate of

1 m^{3} / h

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0.1 m^{3} / h

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1.1 m^{3} / h

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0.5 m^{3} / h

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None of these

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Solution

The correct option is A $1 m^{3} / h$
$\frac{d v}{d t} = 314 m^{3} / h r$ given

Now $V = π r^{2} h$
$\frac{d V}{d t} = π r^{2} \frac{d h}{d t}$
$314 = 3.14 (10)^{2} \frac{d h}{d t}$
$∴ \frac{d h}{d t} = 1 m^{3} / h$

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Q. A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic mere per hour. Then the depth of the wheat is increasing at the rate of (A) 1 m/h (B) 0.1 m/h (C) 1.1 m/h (D) 0.5 m/h

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A cylindrical tank of radius 10m is being filled with wheat at the rate of 314 cubic metre per hour. then the depth of the wheat is increasing at the rate of

The correct option is A 1m3/hdvdt=314m3/hr givenNow V=πr2hdVdt=πr2dhdt314=3.14(10)2dhdt∴dhdt=1m3/h

A cylindrical tank of radius $10 m$ is being filled with wheat at the rate of $314$ cubic metre per hour. then the depth of the wheat is increasing at the rate of

The correct option is A $1 m^{3} / h$
$\frac{d v}{d t} = 314 m^{3} / h r$ given

Now $V = π r^{2} h$
$\frac{d V}{d t} = π r^{2} \frac{d h}{d t}$
$314 = 3.14 (10)^{2} \frac{d h}{d t}$
$∴ \frac{d h}{d t} = 1 m^{3} / h$