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Application of Derivatives
NCERT Class 12
CBSE
Grade 12

Question:

A balloon, which always remains spherical, has a variable radius. Find the rate of increase of its volume with respect to radius when radius is $10\text{ cm}$.

Step-by-Step Solution

$\dfrac{dV}{dr} = 4\pi r^2$. [1.0 Mark]
At $r = 10$: $\dfrac{dV}{dr} = 400\pi\text{ cm}^3/\text{cm}$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Differentiating volume formula: 1.0 Mark
Evaluating rate $= 400\pi$ cm$^3$/cm: 1.0 Mark

Correct Answer:
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