Question

the rectangular pyramid and rectangular prism shown below have the same length, same width, and same height.
complete the following.
(a) find the volume of the pyramid.
\boxed{} \text{m}^3
(b) find the volume of the prism.
\boxed{} \text{m}^3
(c) complete the equation.
volume of the pyramid = \boxed{} \times volume of the prism
when is this equation true?
\bigcirc this equation is true for all rectangular prisms and rectangular pyramids.
\bigcirc this equation is true only for the rectangular prism and rectangular pyramid shown above.
\bigcirc this equation is true for all rectangular prisms and rectangular pyramids with the same length, same width, and same height.

Explanation:

Step1: Calculate pyramid base area

$\text{Base Area} = 6 \times 5 = 30 \, \text{m}^2$

Step2: Compute pyramid volume

$\text{Volume}_{\text{pyramid}} = \frac{1}{3} \times 30 \times 4 = 40 \, \text{m}^3$

Step3: Compute prism volume

$\text{Volume}_{\text{prism}} = 6 \times 5 \times 4 = 120 \, \text{m}^3$

Step4: Find the volume ratio

$\text{Ratio} = \frac{40}{120} = \frac{1}{3}$

Step5: Identify valid condition

The ratio holds when the two shapes have matching length, width, height.

Answer:

(a) $40$
(b) $120$
(c) $\frac{1}{3}$; This equation is true for all rectangular prisms and rectangular pyramids with the same length, same width, and same height.