Question

a solid right pyramid has a square base with an edge length of x cm and a height of y cm. which expression represents the volume of the pyramid? \\(\frac{1}{3}xy\\,\text{cm}^3\\) \\(\frac{1}{3}x^2y\\,\text{cm}^3\\) \\(\frac{1}{2}xy^2\\,\text{cm}^3\\) \\(\frac{1}{2}x^2y\\,\text{cm}^3\\)

Explanation:

Step1: Recall the volume formula for a pyramid

The volume \( V \) of a pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid.

Step2: Calculate the area of the square base

The base of the pyramid is a square with edge length \( x \) cm. The area \( B \) of a square is \( B = \text{side}^2 \), so \( B=x^2 \) \( \text{cm}^2 \).

Step3: Substitute \( B \) and \( h \) into the volume formula

The height \( h \) of the pyramid is \( y \) cm. Substituting \( B = x^2 \) and \( h = y \) into the volume formula \( V=\frac{1}{3}Bh \), we get \( V=\frac{1}{3}\times x^2\times y=\frac{1}{3}x^2y \) \( \text{cm}^3 \).

Answer:

\(\frac{1}{3}x^2y\space \text{cm}^3\) (the second option: \(\boldsymbol{\frac{1}{3}x^2y\space \text{cm}^3}\))