Published by:
CGP EDU Academic Team
Published on: August 14, 2026
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
cm/sec
C
10 cm/sec
D
160 cm/sec
Text Solution
Verified by ExpertsThe correct answer is:
B
Let θ be the semi-vertical angle and r be the radius of the cone at time t. Then,
r = 20 tan θ
⇒ 
= 20 sec 2 θ 
⇒ 
= 20 sec 2 30° × 2 
⇒ 
= 20 × 
× 2 cm/sec = 
cm/sec
Hence is the correct answer.
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