# 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 - Mathematics

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 48cm3, the total surface area of the box is

•  27 cm2

•  32 cm2

• 44 cm2

• 88 cm2

#### 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

6x3 = 48

x= 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 cm

Thus total surface area of the box is  88 cm.

Concept: Surface Area of a Cuboid
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 18 Surface Areas and Volume of a Cuboid and Cube
Exercise 18.3 | Q 6.2 | Page 35

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