Question

If the ratio of length, breadth and height of a cuboidal box is 3 : 2 : 1 and its volume is 384 cc then let us calculate the total surface area of the box

January 1, 2024

Answer

Let the length, breadth & height of the rectangular box be 3x cm, 2x cm & x cm respectively.

According to the problem,

3x . 2x . x = 384

or, 6x³= 384

x³ $=\frac{384}{6}$ = 64 = (4)³

$\therefore$ x = 4

Length = 3 × 4 = 12 cm.

Breadth = 2 × 4 = 8 cm.

& Height = 1 × 4 = 4 cm.

The total area of 6 surfaces of the rectangular parallelopiped

= 2(l × b + l × h + b × h)

= 2(12 × 8 + 12 × 4 + 8 × 4) sqcm.

= 2(96 + 48 + 32) sqcm.

= 2(96 + 48 + 32) sqcm = 2 × 176 sq cm = 352 sq cm

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