Question

Translate the following sentence into a formula:

“One-third the product of the length of the side squared and the height is the volume of a pyramid with a square base”.

Short answer

The formula is $V=\frac{1}{3}{x}^{2}h$.

Step-by-step solution

Step 1. Given information.

The given sentence is:

One-third of the product of the length of the side squared and the height is the volume of the pyramid with a square base.

Step 2. Mention the algebraic variables.

Consider the Volume of the pyramid be V, length of the side be x and the height of the cone be h.

Step 3. Write the formula.

Since the square of the side is $x^2$and one-third of the product of the length of the side squared and the height is $\frac{1}{3}{x}^{2}h$.

Therefore, the formula becomes:

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