CBSE 2026 · Region 5 · Set 3 · Q26 · 3 marks
The volume of a wooden block in the shape of a cube increases at a constant rate as the air becomes moist during the rainy season. Show that the rate of change of its surface area varies inversely as the length of edge of the cube.
Marking-scheme solution
Let x be the length of edge of the cube
Volume $\displaystyle V=x^{3}$
$\displaystyle \dfrac{dV}{dt}=3 x^{2} \dfrac{dx}{dt}=k$ (constant)
Surface area, $\displaystyle S=6 x^{2}$
$\displaystyle \dfrac{dS}{dt}=12 x \dfrac{dx}{dt}=12 x \cdot \dfrac{k}{3 x^{2}}$ using (i)
$\displaystyle =\dfrac{4 k}{x}$
Thus, rate of change of surface area varies inversely as the length of edge of the cube
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CBSE Class 12 Mathematics past-paper question from the 2026board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.