Question
The altitude of a cone is 20 cm and its semivertical 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
BITSAT
Mathematics
Application of Derivatives
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 30 ~cm / sec
- B. 160 3 ~cm / sec
- C. 10 ~cm / sec
- D. 160 ~cm / sec
Answer
B. 160 3 ~cm / sec
Step-by-step solution
Let be the semi-vertical angle and r be the radius of the cone at time t. the radius of the cone at time t. Then, r=20 d r d t =20 ^2 d d t d r d t =20 ^2 30^ 2 [ =30^ . and . d d t =2 ] d r d t =20 4 3 2 ~cm / s = 160 3 ~cm / s
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