Question

find the volume of this square based pyramid.
v = ? cm³

Explanation:

Step1: Recall the volume formula for a square - based pyramid

The volume \( V \) of a square - based pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the square 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 side length \( s = 2\space cm \). The area of a square is \( B=s^{2} \). Substituting \( s = 2\space cm \), we get \( B=(2)^{2}=4\space cm^{2} \).

Step3: Identify the height of the pyramid

From the diagram, the height of the pyramid \( h = 3\space cm \).

Step4: Calculate the volume of the pyramid

Substitute \( B = 4\space cm^{2} \) and \( h=3\space cm \) into the volume formula \( V=\frac{1}{3}Bh \).
\( V=\frac{1}{3}\times4\times3 \)
First, multiply \( 4\times3 = 12 \), then \( \frac{1}{3}\times12 = 4 \).

Answer:

\( 4 \)