https://file.aiquickdraw.com/mathbot/file/1729013052132pv5infpr.jpg

The image shows a rectangular prism (box) with dimensions labeled: width \( w \), length \( l \), and height \( h \). Based on your provided numbers, we can interpret the dimensions as follows:
- \( w = 2 \, \text{in} \) (width),
- \( l = 6 \, \text{in} \) (length),
- \( h = 10 \, \text{in} \) (height).

There are a few typical calculations we can do for a rectangular prism:

### 1. Volume of the Rectangular Prism
The formula for the volume \( V \) of a rectangular prism is:
\[
V = l \times w \times h
\]
Substitute the values:
\[
V = 6 \, \text{in} \times 2 \, \text{in} \times 10 \, \text{in} = 120 \, \text{in}^3
\]

### 2. Surface Area of the Rectangular Prism
The surface area \( S \) of a rectangular prism is given by:
\[
S = 2(lw + lh + wh)
\]
Substitute the values:
\[
S = 2(6 \times 2 + 6 \times 10 + 2 \times 10) = 2(12 + 60 + 20) = 2(92) = 184 \, \text{in}^2
\]

Would you like further details or explanations? Here are some related questions:

1. What is the diagonal length of this rectangular prism?
2. How do changes in dimensions affect the volume?
3. How would the volume be affected if the height were doubled?
4. How do you calculate the lateral surface area of this prism?
5. How do we apply this in practical applications like packaging?

**Tip:** When calculating surface areas, keep track of all the faces to ensure nothing is missed!

Learn how to calculate the volume and surface area of a rectangular prism with dimensions 2 inches by 6 inches by 10 inches. This problem covers essential geometric concepts and is ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation