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Application of Derivatives
Xam Idea
CBSE
Grade 12

Question:

A spherical balloon is being inflated at rate of $35$ cc/sec. Rate of increase of surface area when radius is $10$ cm is:
(a) $7$ sq cm/sec
(b) $3.5$ sq cm/sec
(c) $14$ sq cm/sec
(d) $1.75$ sq cm/sec

Step-by-Step Solution

Key Concept: dV/dt = 4\pi r^2 dr/dt = 35 => dr/dt = 35/(400\pi). dA/dt = 8\pi r dr/dt = 80\pi * 35/(400\pi) = 7.
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Correct Answer: $7$ sq cm/sec
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