Question

what is the height of the prism shown, if its volume is 420 cm³?
84 cm
5 cm
4 cm
7 cm

Explanation:

Step1: Recall prism volume formula

The volume of a rectangular prism is $V = l \times w \times h$, where $l$ = length, $w$ = width, $h$ = height.

Step2: Identify known values

From the diagram, $l=12$ cm, $w=7$ cm, $V=420$ cm³. Substitute into formula:
$420 = 12 \times 7 \times h$

Step3: Calculate product of length & width

$12 \times 7 = 84$, so $420 = 84h$

Step4: Solve for height $h$

$h = \frac{420}{84} = 5$ cm

Answer:

B. 5 cm