What is the volume, in cubic cm, of a rectangular prism with a height of 8cm, a width of 2cm, and a length of 7cm?

1. Break Down the Problem

To find the volume of a rectangular prism, we need to use the formula for volume: $V = l \times w \times h$ where:

• $V$ = Volume
• $l$ = Length
• $w$ = Width
• $h$ = Height

Given:

• Height ($h$) = 8 cm
• Width ($w$) = 2 cm
• Length ($l$) = 7 cm

2. Relevant Concepts

The volume of a rectangular prism is calculated by multiplying its length, width, and height together. This can be expressed mathematically as: $V = l \times w \times h$

3. Analysis and Detail

Substituting the values into the formula: $V = 7 \, \text{cm} \times 2 \, \text{cm} \times 8 \, \text{cm}$

Now calculating step by step:

1. Calculate the area of the base: $\text{Base Area} = l \times w = 7 \, \text{cm} \times 2 \, \text{cm} = 14 \, \text{cm}^2$
2. Now, calculate the volume: $V = \text{Base Area} \times h = 14 \, \text{cm}^2 \times 8 \, \text{cm} = 112 \, \text{cm}^3$

4. Verify and Summarize

We have: $V = 112 \, \text{cm}^3$ This is the volume of the rectangular prism. I've double-checked the calculations, and they confirm the result.

Final Answer

The volume of the rectangular prism is $112 \, \text{cm}^3$.