Question

a solid right pyramid has a square base with an edge length of s units and a height of h units. which expression represents the volume of the pyramid? \\(\frac{1}{4}s^2h\\) units³ \\(\frac{1}{3}s^2h\\) units³ \\(s^2h\\) units³ \\(3s^2h\\) units³

Explanation:

Step1: Calculate base area

The base is a square with side length $s$, so its area is $A = s^2$.

Step2: Apply pyramid volume formula

The volume of a pyramid is $\frac{1}{3} \times \text{base area} \times \text{height}$. Substitute the base area and height $h$:
$$V = \frac{1}{3} \times s^2 \times h = \frac{1}{3}s^2h$$

Answer:

$\boldsymbol{\frac{1}{3}s^2h}$ units³ (corresponding to the second option)