Question

find the volume of this square based pyramid. 6 cm 4 cm 4 cm 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 \( s = 4\space cm \). The area of a square is \( B=s^{2} \). So, \( B = 4^{2}=16\space cm^{2} \).

Step3: Identify the height of the pyramid

From the diagram, the height \( h \) of the pyramid is \( h = 6\space cm \).

Step4: Calculate the volume of the pyramid

Substitute \( B = 16\space cm^{2} \) and \( h = 6\space cm \) into the volume formula \( V=\frac{1}{3}Bh \).
\( V=\frac{1}{3}\times16\times6 \)
First, calculate \( 16\times6 = 96 \), then \( \frac{1}{3}\times96=32 \).

Answer:

\( 32 \)