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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/h
0.1 m/h
1.1 m/h
0.5 m/h
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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 1 m/h.
Explanation:
Let the length of the cylindrical tank be h and the radius be r.
volume of tank = πr2h
= π × 10 × 10 × h ...[∵ r = 10m]
V = 100 π h
rate of change of volume `(dV)/(dt) = 100 pi (dh)/(dt)` ...(1)
314 = 100 `pi (dh)/(dt)`
`therefore (dh)/(dt) = 314/(100 pi) = 314/(100 xx 3.14)` ... [∵ π = 3.14]
= 1 m3 / h
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