Question

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

Explanation:

Step1: Calculate prism volume

Volume = length × width × height
$V_{prism} = 3 \times 2 \times 8$

Step2: Compute prism volume value

$V_{prism} = 48$

Step3: Calculate pyramid volume

Volume = $\frac{1}{3} \times$ base area × height
$V_{pyramid} = \frac{1}{3} \times (3 \times 2) \times 8$

Step4: Compute pyramid volume value

$V_{pyramid} = \frac{1}{3} \times 48 = 16$

Step5: Find volume ratio

Ratio = $\frac{V_{pyramid}}{V_{prism}}$
$\text{Ratio} = \frac{16}{48} = \frac{1}{3}$

Step6: Identify equation validity condition

Match ratio condition to given options.

Answer:

(a) $48$
(b) $16$
(c) $\frac{1}{3}$; This equation is true for all rectangular prisms and rectangular pyramids with the same length, same width, and same height.