Question

The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48cm³, the total surface area of the box is

Options

•  27 cm²

•  32 cm²

• 44 cm²

• 88 cm²

Answer 1

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

         6x³ = 48

           x³ = 8

           x = 2

Thus,

Surface area of the box,

= 2 (lb+bh+hl)

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

= 2 (11x²)

= 22 x²

= 22 (2)^²

= 88 cm² 

Thus total surface area of the box is  88 cm² .