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Updated on : 2022-09-05

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Correct option is B)

Let the breadth be $x$, length be $2x$ and height be $h$

$V=x.2x.h$

$⇒c=2x_{2}h$ ....(1)

Area of bottom $=2x_{2}$ =Area of top

Area of sides $=2xh+2xh+xh+xh=6xh.$

If R rupees be the cost of material for bottom then for the top and sides is 3R.

$∴E=R(2x_{2})+3R(2x_{2}+6xh)$

$⇒E=R(8x_{2}+18xh)$

or $E=R(8x_{2}+18x2x_{_{2}}c )$

$⇒E=R(8x_{2}+x9c )$

where R and c are constants.

$dxdE =R(16x−x_{2}9c )$

For maximum or minimum,

$dxdE =0$

$∴x=(169c )_{1/3}$

Also, $dx_{2}d_{2}E =R(16+x_{3}18c )=+ive$

and hence minimum.

$∴$ dimensions are

$[169c ]_{1/3},2[169c ]_{1/3}$ and $[8132c ]_{1/3}.$

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