Question

Do the two solids have the same volume? Explain.

Answer 1

Hint: Find the volume of the shapes & then compare the volume.

Step 1: Here, We are given with two type of solids. One is rectangular pyramids and the other one is triangular pyramid.

Step 2: The formula of the volume of the prism is given by: $V=Bh$

Where, $B$ is the area of the base & $h$ is the height of the prism

Now, The base is rectangular in shape.

$B=(l\times w)$

Here, In the question $l=x,w=y\&h=z$

$$\begin{gathered} V=(x\times y)\left(z\right) \\ B=xyz \end{gathered}$$

Step 3: The formula of the volume of the pyramid is given by: $V=\frac{1}{3}Bh$

Where, $B$ is the area of the base & $h$ is the height of the pyramid

$V=\frac{1}{3}\left(xy\right)\left(3z\right)$

Cancel the common terms.

$V=xyz$

Step 4: Since the obtained volume of the rectangular prism $V=xyz$ is the same as the simplified volume of the pyramid $V=xyz$, the volume of the solids are equal

Final Answer: Hence, The volume of the solids are equal.