The edges of a cuboid are in the ratio 1: 2: | vedclass

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(B) Let the edges of the cuboid be $l = 3x,$ $b = 2x,$ and $h = x.$The surface area of a cuboid is given by the formula $2(lb + bh + lh) = 88 \, cm^2.

Vedclass · Accepted Answer

$48$

Vedclass · Answer

(B) Let the edges of the cuboid be $l = 3x,$ $b = 2x,$ and $h = x.$The surface area of a cuboid is given by the formula $2(lb + bh + lh) = 88 \, cm^2.$Substituting the values,we get $2((3x)(2x) + (2x)(x) + (3x)(x)) = 88.$$2(6x^2 + 2x^2 + 3x^2) = 88.$$2(11x^2) = 88.$$22x^2 = 88.$$x^2 = 4 \implies x = 2 \, cm.$Now,the dimensions are $l = 3(2) = 6 \, cm,$ $b = 2(2) = 4 \, cm,$ and $h = 2 \, cm.$The volume of the cuboid is $V = l 	imes b 	imes h = 6 	imes 4 	imes 2 = 48 \, cm^3.$

The edges of a cuboid are in the ratio $1: 2: 3,$ and its surface area is $88 \, cm^2.$ The volume of the cuboid is ........ $cm^3$.

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