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