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^2 h\\) units\\(^3\\)
one-third \\(s^2 h\\) units\\(^3\\)
\\(s^2 h\\) units\\(^3\\)
\\(3 s^2 h\\) units\\(^3\\)

Explanation:

Identify the base area

The base of the right pyramid is a square with side length \(s\).
The area of a square base \(B\) is:

$$B = s^2$$

Apply the pyramid volume formula

The volume \(V\) of any pyramid is given by:

$$V = \frac{1}{3} \cdot B \cdot h$$

where \(B\) is the base area and \(h\) is the height.

Substitute the base area

Substitute \(B = s^2\) into the volume formula:

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

Match with the given options

The expression \(\frac{1}{3} s^2 h\) is written in words as "one-third \(s^2 h\)".
This matches the second option.

Answer:

• (A) \(\frac{1}{4}s^2h\text{ units}^3\)
• (B) \(\text{one-third } s^2h\text{ units}^3\) (Correct answer)
• (C) \(s^2h\text{ units}^3\)
• (D) \(3s^2h\text{ units}^3\)