TS EAMCET · Maths · Application of Derivatives
If the radius of a spherical balloon is increasing at the rate of inch per minute, then the rate at which the volume increases (in cube inches per minute) when the radius is inches is
- A
- B
- C
- D
Answer & Solution
Correct Answer
(C)
Step-by-step Solution
Detailed explanation
Given, drdt=5 inch/minute r=10 inches Volume of spherical balloon is V=43πr3 Differentiating w. r. t. t ddtV=ddt43πr3 dVdt=43×3πr2drdt dVdt=4π×100×5 dVdt=2000π cubic inches per minute
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