Question

A cuboid has length = 4 cm, breadth = 3 cm and diagonal = 13 cm. The volume of the cuboid is ______.

Options

• 156 cm³

• 288 cm³

• 144 cm³

• 78 cm³

Answer 1

A cuboid has length = 4 cm, breadth = 3 cm and diagonal = 13 cm. The volume of the cuboid is 144 cm³.

Explanation:

The diagonal of a cuboid is given by \[d = \sqrt{l^2 + b^2 + h^2}\]. Substituting the given values: \[13 = \sqrt{4^2 + 3^2 + h^2} \implies 13 = \sqrt{25 + h^2}\]. Squaring both sides yields \[169 = 25 + h^2\], so \[h^2 = 144\] giving height \[h = 12\text{ cm}\]. The volume is \[l \times b \times h = 4 \times 3 \times 12 = 144\text{ cm}^3\].