COMEDK · Maths · 27. Application of Derivatives
The side of a cube is equal to the diameter of a sphere. If the side and radius increase at the same rate then the ratio of the increase of their surface area is
- A \(2 \pi: 3\)
- B \(3: 2 \pi\)
- C \(3: \pi\)
- D \(\pi: 6\)
Answer & Solution
Correct Answer
(C) \(3: \pi\)
Step-by-step Solution
Detailed explanation
Let the side of the cube be \(a\) and the radius of the sphere be \(r\). Given that the side of the cube is equal to the diameter of the sphere, we have \(a = 2r\). Let the rate of increase of the side and the radius be \(\dfrac{da}{dt} = \dfrac{dr}{dt} = k\). The surface area…
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