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.
\square m^3
(b) find the volume of the prism.
\square m^3
(c) complete the equation.
volume of the prism = \square \times volume of the pyramid
when is this equation true?
\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.
\bigcirc this equation is true for all rectangular prisms and rectangular pyramids.

Explanation:

Step1: Calculate pyramid base area

$\text{Base Area} = 5 \times 3 = 15 \, \text{m}^2$

Step2: Compute pyramid volume

$V_{\text{pyramid}} = \frac{1}{3} \times 15 \times 6 = 30 \, \text{m}^3$

Step3: Compute prism volume

$V_{\text{prism}} = 5 \times 3 \times 6 = 90 \, \text{m}^3$

Step4: Find prism-pyramid volume ratio

$\frac{V_{\text{prism}}}{V_{\text{pyramid}}} = \frac{90}{30} = 3$

Step5: Identify valid condition

The ratio holds when length, width, height are equal for both shapes.

Answer:

(a) $30$
(b) $90$
(c)
Volume of the prism $= 3 \times$ Volume of the pyramid
Correct option: This equation is true for all rectangular prisms and rectangular pyramids with the same length, same width, and same height.