Question

The edges of a cuboid have their volumes in the ratio 1:2:3 and its surface area is 88cm². The volume of the cuboid is

(a) 48 cm³ (b) 64 cm³ (c) 96 cm³ (d) 120 cm³

Answer 1

(a) 48 cm³

Explanation:

Let a be the length of smallest edge.

The edges are in the proportion a: 2a: 3a

We know that total surface area of cuboid= 2(l b + b h + h l)

Surface area = 2 (2 a² + 3 a² + 6 a²)

88 = 22 a²

a = 2

2a=4

3a = 6

We know that volume of cuboid= length × breadth × height

V = 2 × 4 × 6

V = 48