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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]

Sagot :

GinnyAnswer
To find the volume of a solid right pyramid with a square base, we need to follow a few steps and apply the appropriate formula.

1. Understand the given parameters:
- The edge length of the square base is [tex]\( x \)[/tex] cm.
- The height of the pyramid is [tex]\( y \)[/tex] cm.

2. Determine the area of the base:
- The base of the pyramid is a square with edge length [tex]\( x \)[/tex].
- The area of a square is calculated as the side length squared.
[tex]\[ \text{Base area} = x^2 \, \text{cm}^2 \][/tex]

3. Recall the volume formula for 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]

4. Substitute the known values into the formula:
- We already calculated the base area as [tex]\( x^2 \)[/tex].
- The height of the pyramid is given as [tex]\( y \)[/tex].
- Plug these into the volume formula:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]

5. Final expression:
- The volume of the pyramid is:
[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]\[ \boxed{\frac{1}{3} x^2 y \, \text{cm}^3} \][/tex]
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