Question

what is the formula for the volume of a pyramid with h = w?
○ $v = \frac{1}{2}bw$
○ $v = \frac{1}{3}bw$
○ $v = \frac{1}{3}\pi r^2 w$
○ $v = bw$
○ $v = 4\pi r^2$

Explanation:

Step1: Recall Pyramid Volume Formula

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

Step2: Substitute \( h = w \)

Given \( h = w \), substitute \( h \) with \( w \) in the formula. So the formula becomes \( V=\frac{1}{3}Bw \).

Step3: Eliminate Other Options

• Option \( V=\frac{1}{2}Bw \): The coefficient \( \frac{1}{2} \) is incorrect for pyramid volume.
• Option \( V=\frac{1}{3}\pi r^{2}w \): This is the volume formula for a cone (since it has \( \pi r^{2} \) for circular base), not a pyramid.
• Option \( V = Bw \): This would be the volume of a prism (no \( \frac{1}{3} \) factor), not a pyramid.
• Option \( V = 4\pi r^{2} \): This is the surface area formula for a sphere, not a volume formula for a pyramid.

Answer:

B. \( V=\frac{1}{3}Bw \)