Question

1. what is the missing height of the prism below if the volume is 455 cubic feet?

find the volume if the edge lengths are \\( \frac{1}{3} \\)

Explanation:

Step1: Recall prism volume formula

$V = l \times w \times h$

Step2: Solve question 13 for missing height

Rearrange formula: $h = \frac{V}{l \times w}$
Substitute values: $h = \frac{455}{6 \times 9} = \frac{455}{54} \approx 8.42$

Step3: Calculate new edge lengths

New edges: $l' = \frac{6}{3}=2$, $w' = \frac{9}{3}=3$, $h' = \frac{455/54}{3}=\frac{455}{162}$

Step4: Compute new volume

$V' = 2 \times 3 \times \frac{455}{162} = \frac{2730}{162} \approx 8.426$

Answer:

8.426 cubic feet (for the second question), 8.42 ft (for question 13, rounded to two decimal places)