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Question

Water poured into an inverted conical vessel of which the radius of the base is 2 m and height 4 m, and the rate of 77 litres/minute. The rate at which the water level is rising at the instant when the depth is 70 cm is: (use π=22/7)

A
10cm/min
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B
20cm/min
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C
40cm/min
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D
None
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Solution

The correct option is B 20cm/min
Given,
R=2m=200cm

H=4m=400cm

1Litre=1000cm3

V=volume of Cone

dVdt=77litreminute

dVdt=77×1000cm3minute

VolumeofCone=13×227×r2h

Differentiating V with respect to t keeping r as constant and h as variable,

dVdt=13×227×r2×dhdt

dhdt=dVdt×3×722×1r2

=77×1000cm3minute×3×722×1(200cm)2

=14780cmmin


956174_1023005_ans_4041aa18b1194ea4932e192d5f0e8378.png

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