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.
- Step 1: The volume of a sphere is . Differentiating with respect to gives .
- 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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