COMEDK · Maths · 27. Application of Derivatives
If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is
- A proportional to the radius
- B inversely proportional to its surface area
- C inversely proportional to the radius
- D a constant
Answer & Solution
Correct Answer
(B) inversely proportional to its surface area
Step-by-step Solution
Detailed explanation
The volume \(V\) of a sphere of radius \(r\) is given by \(V = \dfrac{4}{3} \pi r^{3}\). Differentiating both sides with respect to time \(t\), we get \(\dfrac{dV}{dt} = 4 \pi r^{2} \dfrac{dr}{dt}\). It is given that the volume is increasing at a constant rate, so…
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