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Q.

A square piece of tin of side $30 c m$ is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the volume of the box is maximum, then its surface area (in $c m^{2}$ ) is equal to

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a

$900$

b

$1025$

c

$800$

d

$675$

answer is C.

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Detailed Solution

Volume (V) = $x {(30 - 2 x)}^{2}$
$\frac{d V}{d x} = {(30 - 2 x)}^{2} - 4 (30 - 2 x) x$
$= (30 - 2 x) (30 - 6 x)$
$\frac{d V}{d x} = 0$
$\Rightarrow x = 5 c m$ , which is point of maxima.
$∴$ Surface area = $4 \times 5 \times 20 + {(20)}^{2} = 800 c m^{2}$

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