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

Correct option is D. 88 cm²

Given,

Ratio of length , width and height of rectangular solid = 3 : 2 : 1

Volume of box = 48 cm³

Let length of box = 3x cm

Breadth of box = 2x cm

Height of box = x cm

Volume of box = v = 3x \(\times\) 2x \(\times\) x = 48

= 6x³ = \(\cfrac{48}6\) = 8

= x = \(\sqrt[3]{8}\) = 2 cm

Hence . length = 3x = 3 ×2 = 6 cm

= breadth = 2x = 2 × 2 = 4 cm

= height = x = 2 cm

Total surface area of box = 2(lb + bh + hl) = 2(24 + 8 + 12)

= 88 cm²