TS EAMCET · Maths · Differential Equations
The volume of a spherical balloon is increasing at the rate of When its radius is the rate of change of its surface area (in ) is
- A
- B
- C
- D
Answer & Solution
Correct Answer
(A)
Step-by-step Solution
Detailed explanation
Let V be the volume & S be the surface area of spherical balloon having radius r. Given:dVdt=2cm3/sec To find:dSdtr=4 As, volume V=43πr3 ⇒dVdt=433πr2drdt ⇒2=433πr2drdt ∴drdt=12πr2 Now, S=4πr2 ⇒dSdt=4π×2rdrdt…
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