Answered

A solid right pyramid has a square base with an edge length of [tex]x \, \text{cm}[/tex] and a height of [tex]y \, \text{cm}[/tex].

Which expression represents the volume of the pyramid?

A. [tex]\frac{1}{3} x y \, \text{cm}^3[/tex]

B. [tex]\frac{1}{3} x^2 y \, \text{cm}^3[/tex]

C. [tex]\frac{1}{2} x y^2 \, \text{cm}^3[/tex]

D. [tex]\frac{1}{2} x^2 y \, \text{cm}^3[/tex]



Answer :

GinnyAnswer
Let's determine the correct expression for the volume of a solid right pyramid that has a square base with an edge length of [tex]\(x\)[/tex] cm and a height of [tex]\(y\)[/tex] cm.

1. Identify the base area of the pyramid:
- The base of the pyramid is square, so to find the area of the square base, we use the formula for the area of a square, which is:
[tex]\[ \text{Area of the base} = x^2 \text{ cm}^2 \][/tex]

2. Recall the formula for the volume of a pyramid:
- The volume [tex]\(V\)[/tex] of a pyramid is given by:
[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]

3. Substitute the values in the formula:
- We already know that the base area is [tex]\(x^2\)[/tex] and the height is [tex]\(y\)[/tex]. Substituting these into the volume formula, we get:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]

4. Simplify and express the volume:
- Simplifying this, the volume of the pyramid becomes:
[tex]\[ V = \frac{1}{3} x^2 y \text{ cm}^3 \][/tex]

Therefore, the correct expression that represents the volume of the pyramid is:
[tex]\[ \frac{1}{3} x^2 y \text{ cm}^3 \][/tex]

The correct choice is:
[tex]\[ \boxed{\frac{1}{3} x^2 y \text{ cm}^3} \][/tex]

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