A spherical balloon is being inflated so that its volume increases at a constant rate of . Find the rate of increase of its radius when the radius is .

Answer and explanation

Correct answer: B.

  1. Step 1: The volume of a sphere is . Differentiating with respect to gives .
  2. Step 2: By the chain rule, . Substitute and : .
Answer
.
Why not the others: The rate divides by instead of ; the rate divides by ; the rate confuses the radius value with the rate of increase.

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