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Question

The altitude of a cone is 20 cm and its semi-vertical angle is 30. If the semi-vertical angle is increasing at the rate of 2 per second, then the radius of the base is increasing at the rate of


A

30 cm/sec

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B

160/3 cm/sec

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C

10 cm/sec

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D

160 cm/sec

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Solution

The correct option is B

160/3 cm/sec


Let θ be the semi-vertical angle and r be the radius of the cone at time t. Then,
r=20tanθ
drdt=20sec2θdθdt

drdt=20sec230×2[θ=30anddθdt=2]drdt=20×43×2cm/sec
Hence (b) is the correct answer

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