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Applied Mathematics · 2025 · 4 marks
CBSE 2025 · Central · Set 4 · Q36
A man has an expensive square-shaped piece of golden board of side 36 cm. He wants to turn it into a box without top by cutting a square from each…
A man has an expensive square-shaped piece of golden board of side $\displaystyle 36$ cm. He wants to turn it into a box without top by cutting a square from each corner and folding the flaps. Let $\displaystyle x$ cm be the side of square, which is cut from each corner.
Based on the above information, answer the following questions :
(i)
Find the expression for the volume (V) of open box in terms of $\displaystyle x$.
(ii)
Find $\displaystyle \frac{\mathrm{dV}}{\mathrm{d} x}$.
(iii)
Find the value of $\displaystyle x$ for which the volume (V) is maximum.
OR
(iii)
Find the maximum volume of the open box.
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CBSE Class 12 Applied Mathematics past-paper question from the 2025 board exam. Where our answers come from.