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
To find the volume of a solid right pyramid with a square base, we need to use the volume formula for a pyramid. The formula for the volume [tex]\( V \)[/tex] of a pyramid is given by:

[tex]\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \][/tex]

Let's break down the components of this formula step by step:

1. Determine the Base Area:
The base of the pyramid is a square with an edge length of [tex]\( x \)[/tex] cm. The area of a square is given by:
[tex]\[ \text{Base Area} = \text{edge length}^2 = x^2 \][/tex]

2. Determine the Height:
The height of the pyramid is given as [tex]\( y \)[/tex] cm.

3. Substitute the Base Area and Height into the Volume Formula:
Using the base area [tex]\( x^2 \)[/tex] and height [tex]\( y \)[/tex], we substitute these into the volume formula:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \][/tex]

Thus, the expression for the volume of the pyramid is:
[tex]\[ V = \frac{1}{3} x^2 y \text{ cm}^3 \][/tex]

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