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MCQ

The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm^{3}, the total surface area of the box is

#### Options

27 cm

^{2}32 cm

^{2}44 cm

^{2}88 cm

^{2}

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#### Solution

Length (*l*), width (*b*) and height (*h*) of the rectangular solid are in the ratio 3 : 2 : 1.

So we can take,

(l) = 3x cm

(b) = 2 x cm

(h) = x cm

We need to find the total surface area of the box

Volume of the box,

`V= 48 cm^3`

lbh = 48

(3x)(2x)x = 48

6x^{3} = 48

x^{3 }= 8

x = 2

Thus,

Surface area of the box,

= 2 (lb+bh+hl)

= 2 [(3x)(2x)+(2x) x +(x)(3x)]

= 2 (11x^{2})

= 22 x^{2}

= 22 (2)^^{2}

= 88 cm^{2 }

Thus total surface area of the box is 88 cm^{2 }.

Concept: Surface Area of a Cuboid

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