A right prism has a volume of 112 cm3. If it has a height of 2 cm and a width of 8 cm, then its length is

1. Break Down the Problem

To find the length of the right prism, we need to use the formula for the volume of a prism: $\text{Volume} = \text{Base Area} \times \text{Height}$ The base area can be determined using the width and length: $\text{Base Area} = \text{Width} \times \text{Length}$

Given:

• Volume $V = 112 \, \text{cm}^3$
• Height $h = 2 \, \text{cm}$
• Width $w = 8 \, \text{cm}$

2. Relevant Concepts

The formula relating volume, height, and base area will be used to isolate the length. We can rewrite the volume formula: $V = w \times l \times h$ where $l$ is the length of the prism.

3. Analysis and Detail

We can substitute the known values into the volume formula and solve for $l$: $112 = 8 \times l \times 2$ We can simplify the equation:

1. Calculate $8 \times 2 = 16$: $112 = 16 \times l$
2. Now, isolate $l$: $l = \frac{112}{16}$

4. Verify and Summarize

Calculating $\frac{112}{16}$: $l = 7 \, \text{cm}$ Therefore, the length of the right prism is confirmed through the calculations.

Final Answer

The length of the prism is $7 \, \text{cm}$.