https://file.aiquickdraw.com/mathbot/file/1729092707392i517gz1d.jpg

The image shows a rectangular prism (also called a cuboid) with labeled dimensions \( l \), \( w \), and \( h \), where:

- \( l \) (length) = 10 inches
- \( w \) (width) = 6 inches
- \( h \) (height) = 2 inches

We can calculate two key properties of this cuboid:

1. **Volume**: The volume \( V \) of a rectangular prism is given by the formula:
   \[
   V = l \times w \times h
   \]
   Substituting the given values:
   \[
   V = 10 \times 6 \times 2 = 120 \, \text{in}^3
   \]
   So, the volume is **120 cubic inches**.

2. **Surface Area**: The surface area \( A \) of a rectangular prism is calculated using the formula:
   \[
   A = 2(lw + lh + wh)
   \]
   Substituting the given values:
   \[
   A = 2(10 \times 6 + 10 \times 2 + 6 \times 2) = 2(60 + 20 + 12) = 2 \times 92 = 184 \, \text{in}^2
   \]
   So, the surface area is **184 square inches**.

Would you like more details or have any other questions?

Here are some related questions for further exploration:

1. What would the volume be if the height were doubled?
2. How does changing the width affect the surface area?
3. If the cuboid were filled with a material, how much material would it hold in cubic centimeters?
4. What is the diagonal length of the cuboid?
5. Can you form a cube with the same surface area as this cuboid?

**Tip**: The surface area of a rectangular prism grows faster than its volume as dimensions increase.

The query submitted by the user: 2in 6in 10in

Learn how to calculate the volume and surface area of a rectangular prism with dimensions 10 inches by 6 inches by 2 inches. This geometry problem teaches key concepts such as the volume formula (V = l × w × h) and surface area formula (A = 2(lw + lh + wh)), suitable for 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