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 48 cm³ , the total surface area of the box is
A. 27 cm²
B. 32 cm²
C. 64 cm²
D. 88 cm²

Answer 1

Answer:

88cm^2

Answer strp by step

let the length,bwidth and height be 3x,2x,x.

volume =48cm^3

3x*2x*x=48

6x^3=48

x^3=8

x=2

total surface area

2(lb+bh+lh)

2(3x*2x+2x*x+3x*x)

2(6x^2+2x^2+3x^2)

2(11x^2)

put the value of x

2(11*2*2)

88cm^2

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Answer 2

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

Let the length of box, l = 3x cm

Breadth of box , b = 2x cm

Height of box , h = x cm

Volume of box ,V  = l × b × h  

48 = 3x × 2x × x  

48 = 6x³

x³ = 48/6

x³ = 8  

x = ³√8

x = 2 cm

So, length ,l = 3x = 3 × 2 = 6 cm

breadth ,b = 2x = 2 × 2 = 4 cm

height ,h = x = 2 cm

Now,Total surface area of box , T.S.A = 2(lb + bh + hl)  

T.S.A of a box = 2(6 × 4 + 4 × 2 + 2 × 6)

T.S.A of a box = 2(24 + 8 + 12)

T.S.A of a box = 2(44) = 88 cm²

Total surface area of box  = 88 cm²

Hence, the total surface area of the box is 88 cm².

Option (D) 88 cm² is correct.

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