The altitude of a cone is 20 cm and its semi-vertical a
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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
B.
1603cm/sec
C.
10 cm/sec
D.
160 cm/sec
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
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