The edges of a cuboid are in the ratio 1: 2: 3 and its surface area is 88 cm2. The volume of the cuboid is
Let a be the length of the smallest edge
Therefore,
The edges are in proportion a: 2a: 3a
We know that,
Surface area of cuboid = 2 (lb + bh + hl)
= 2 (a × 2a + a × 3a + 2a × 3a)
= 2 (2a2 + 3a2 + 6a2)
= 22a2
= 88 cm2
a =
= = 2
Also,
2a = 2 × 2 = 4
And,
3a = 3 × 2 = 6
Therefore,
Volume = a × 2a × 3a
= 2 × 4 × 6
= 48 cm3
Hence, option A is correct