The base of a right pyramid is a square of side \(12\sqrt{2}\) cm, and each of its slant edges is 15 cm long. What is the volume of the pyramid?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 864 cm3
In a right pyramid the top vertex is directly above the centre of the base. A slant edge, the height and the half-diagonal of the base form a right triangle. The volume of a pyramid is \(\displaystyle\frac{1}{3}\times\) base area \(\times\) height.
Diagonal of the base \(=12\sqrt{2}\times\sqrt{2}=24\) cm, so half-diagonal \(=12\) cm
Height \(=\sqrt{15^2-12^2}=\sqrt{225-144}=\sqrt{81}=9\) cm
Base area \(=(12\sqrt{2})^2=288\) cm2
Volume \(\displaystyle=\frac{1}{3}\times288\times9=864\) cm3
