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Application of Derivatives
NCERT Class 12
CBSE
Grade 12

Question:

If the volume of a cube is increasing at the rate of $9\text{ cm}^3/\text{s}$, how fast is the surface area increasing when edge length is $10\text{ cm}$?
(a) $3.6\text{ cm}^2/\text{s}$
(b) $1.8\text{ cm}^2/\text{s}$
(c) $4.5\text{ cm}^2/\text{s}$
(d) $2.4\text{ cm}^2/\text{s}$

Step-by-Step Solution

$\dfrac{dS}{dt} = \dfrac{36}{x} = \dfrac{36}{10} = 3.6$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Evaluating $dS/dt = 3.6$ cm$^2$/s: 1.0 Mark

Correct Answer: $3.6\text{ cm}^2/\text{s}$
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