The base of a right pyramid is a square of side \(8\sqrt{2}\) cm, and each of its slant edges is 10 cm long. What is the volume of the pyramid?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 256 cm3
In a right pyramid the top is directly above the centre of the base. The height, half a diagonal of the base and a slant edge form a right triangle. Then the volume is \(\frac{1}{3}\times\) base area \(\times\) height.
Diagonal of the base \(=8\sqrt{2}\times\sqrt{2}=16\) cm, so half the diagonal \(=8\) cm
Height \(=\sqrt{10^2-8^2}=\sqrt{100-64}=6\) cm
Base area \(=\left(8\sqrt{2}\right)^2=128\) cm2
Volume \(=\displaystyle\frac{1}{3}\times128\times6=256\) cm3
