Q19. - Geometry

Question

The shaded pyramid in the diagram is cut from a rectangular solid. How does the volume of the pyramid compare with the volume of the rectangular solid?

Step-by-Step Solution

Answer

The volume of pyramid is one sixth times of the volume of rectangular solid.

Step 1. Given information.

The figure provided in the question,

Step 2. Write the concept.

The volume of the rectangle solid,

$v_r=lbh$

Step 3. Determine the volume.

Now, find the volume of pyramid.

$\begin{array}{c}{v}_p=\frac{1}{3}\left(l\right)\left(\frac{1}{2}bh\right)\\ v_p=\frac{1}{6}lbh\text{ [multiply]}\\ v_p=\frac{1}{6}{v}_r\end{array}$

This shows that, the volume of pyramid is one sixth times of the volume of rectangular solid.