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Question
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
Options
1 m/hr
0.1 m/hr
1.1 m/hr
0.5 m/hr
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Solution
1 m/hr
\[\text { Let r, hand V be the radius, height and volume of the cylinder at any time t. Then },\]
\[V = \pi r^2 h\]
\[ \Rightarrow \frac{dV}{dt} = \pi r^2 \frac{dh}{dt}\]
\[ \Rightarrow 314 = 3 . 14 \times \left( 10 \right)^2 \frac{dh}{dt}\]
\[ \Rightarrow \frac{dh}{dt} = \frac{314}{314}\]
\[ \Rightarrow \frac{dh}{dt} = 1 m/hr\]
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