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(C) Let the dimensions of the cuboid be $4x$,$3x$,and $1x$.The total surface area of a cuboid is given by the formula: $TSA = 2(lb + bh + lh)$.Substit

Vedclass · Accepted Answer

$12000$

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(C) Let the dimensions of the cuboid be $4x$,$3x$,and $1x$.The total surface area of a cuboid is given by the formula: $TSA = 2(lb + bh + lh)$.Substituting the given values: $3800 = 2((4x)(3x) + (3x)(x) + (4x)(x))$.$3800 = 2(12x^{2} + 3x^{2} + 4x^{2})$.$3800 = 2(19x^{2})$.$3800 = 38x^{2}$.$x^{2} = 100$,which implies $x = 10 \, cm$.The dimensions are $4(10) = 40 \, cm$,$3(10) = 30 \, cm$,and $1(10) = 10 \, cm$.The volume of the cuboid is $V = l 	imes b 	imes h = 40 	imes 30 	imes 10 = 12,000 \, cm^{3}$.

The dimensions of a cuboid are in the ratio of $4: 3: 1$. If its total surface area is $3800 \, cm^{2}$,then find its volume in $cm^{3}$.

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