Question

The dimensional ratio of the sides of a cuboid is 3 : 2 : 1. If its volume is 1296 cm³: the actual dimensions of the cuboid are ______.

Options

• 12 cm, 12 cm and 8 cm

• 8 cm, 8 cm and 12 cm

• 12 cm, 12 cm and 12 cm

• 18 cm, 12 cm and 6 cm

Answer 1

The dimensional ratio of the sides of a cuboid is 3 : 2 : 1. If its volume is 1296 cm³: the actual dimensions of the cuboid are 18 cm, 12 cm and 6 cm.

Explanation:

Let the dimensions of the cuboid be 3x, 2x, and x. The volume is \[(3x)(2x)(x) = 6x^3 = 1296\text{ cm}^3\], which means x³ = 216 and x = 6 cm. Multiplying this by the ratio gives the dimensions: 3(6) = 18 cm, 2(6) = 12 cm, and 1(6) = 6 cm.