COMEDK · Maths · 27. Application of Derivatives
A spherical snowball is melting such that its volume is decreasing at the rate of \(1 \mathrm{~cm}^3 / \mathrm{min}\). The rate at which the diameter is decreasing when the diameter is 10 cm is
- A \(\dfrac{2}{75 \pi} \mathrm{~cm} / \mathrm{min}\)
- B \(\dfrac{1}{50 \pi} \mathrm{~cm} / \mathrm{min}\)
- C \(\dfrac{11}{75 \pi} \mathrm{~cm} / \mathrm{min}\)
- D \(\dfrac{1}{25 \pi} \mathrm{~cm} / \mathrm{min}\)
Answer & Solution
Correct Answer
(B) \(\dfrac{1}{50 \pi} \mathrm{~cm} / \mathrm{min}\)
Step-by-step Solution
Detailed explanation
Let \(V\) be the volume and \(D\) be the diameter of the spherical snowball. The volume of a sphere is given by \(V = \dfrac{4}{3} \pi r^3\), where \(r\) is the radius. Since \(D = 2r\), we have \(r = \dfrac{D}{2}\). Substituting \(r\) in terms of \(D\),…
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