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Volume of Pyramids

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 determine which expression represents the volume of a right pyramid with a square base, let's go through the formula for the volume of the pyramid step by step:

1. Identify the base area:
- The base of the pyramid is a square.
- If the edge length of the square base is [tex]\( x \)[/tex] cm, then the area of the square base ([tex]\( A \)[/tex]) is:
[tex]\[ A = x^2 \text{ cm}^2 \][/tex]

2. Identify the height:
- The height of the pyramid ([tex]\( h \)[/tex]) from the base to the apex is given as [tex]\( y \)[/tex] cm.

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

4. Substitute the base area and height into the formula:
- Using the base area [tex]\( x^2 \)[/tex] and the height [tex]\( y \)[/tex], we have:
[tex]\[ V = \frac{1}{3} \times x^2 \times y \text{ cm}^3 \][/tex]

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

So, the correct answer is:
[tex]\[ \boxed{\frac{1}{3} x^2 y \text{ cm}^3} \][/tex]
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