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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 (A) 1 M/Hr (B) 0.1 M/Hr (C) 1.1 M/Hr - CBSE (Science) Class 12 - Mathematics

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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

  • 1 m/hr

  •  0.1 m/hr

  • 1.1 m/hr

  •  0.5 m/hr

Solution

 1 m/hr

\[\text { Let r, hand V be the radius, height and volume of the cylinder at any time t. Then },\]

\[V = \pi r^2 h\]

\[ \Rightarrow \frac{dV}{dt} = \pi r^2 \frac{dh}{dt}\]

\[ \Rightarrow 314 = 3 . 14 \times \left( 10 \right)^2 \frac{dh}{dt}\]

\[ \Rightarrow \frac{dh}{dt} = \frac{314}{314}\]

\[ \Rightarrow \frac{dh}{dt} = 1 m/hr\]

  Is there an error in this question or solution?
Solution 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 (A) 1 M/Hr (B) 0.1 M/Hr (C) 1.1 M/Hr Concept: Rate of Change of Bodies Or Quantities.
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