Question

A pyramid has a square base with sides of length s. The height of the pyramid is equal to - of the length of a side on the base. Which formula
represents the volume of the pyramid?

Answer 1

Question:

A pyramid has a square base with sides of length s. The height of the pyramid is equal to 1/2 of the length of a side on the base. Which formula represents the volume of the pyramid?

Answer:

The formula represents the volume of the pyramid is:

$V=\frac{1}{6}s^3$

Solution:

The volume of square pyramid is given by formula:

$V = \frac{1}{3} a^2h$

Where, "h" is the height of pyramid

"a" is the length of side of base

Here given that, pyramid has a square base with sides of length s

Therefore,

a = s

The height of the pyramid is equal to 1/2 of the length of a side on the base

$h = \frac{1}{2} \times s\\\\h = \frac{s}{2}$

Thus the volume of pyramid becomes:

$V = \frac{1}{3} \times s^2 \times \frac{s}{2}\\\\V = \frac{s^3}{6}$

$\boxed{V=\frac{1}{6}s^3}$

Thus the  formula  represents the volume of the pyramid is $\frac{s^3}{6}$