https://file.aiquickdraw.com/mathbot/file/1725445074573o75qft12.jpg

The image provided seems to contain a problem related to geometry, specifically dealing with the volume and surface area of a rectangular prism. I'll interpret and solve the problem based on what I can extract from the image.

### Problem Summary:
- **Given:** A rectangular prism with dimensions \( l = 7 \) cm, \( w = 4 \) cm, and \( h = 3 \) cm.
- **Tasks:**
  1. Calculate the volume of the rectangular prism.
  2. Calculate the surface area of the rectangular prism.

### Step-by-Step Solution:

#### 1. Volume of the Rectangular Prism

The formula for the volume \( V \) of a rectangular prism is:
\[
V = l \times w \times h
\]
Where:
- \( l = 7 \) cm (length),
- \( w = 4 \) cm (width),
- \( h = 3 \) cm (height).

Substituting the values:
\[
V = 7 \times 4 \times 3 = 28 \times 3 = 84 \, \text{cm}^3
\]

So, the volume of the rectangular prism is **84 cm³**.

#### 2. Surface Area of the Rectangular Prism

The formula for the surface area \( A \) of a rectangular prism is:
\[
A = 2(lw + lh + wh)
\]
Where:
- \( l = 7 \) cm,
- \( w = 4 \) cm,
- \( h = 3 \) cm.

First, calculate each of the products inside the parentheses:
\[
lw = 7 \times 4 = 28 \, \text{cm}^2
\]
\[
lh = 7 \times 3 = 21 \, \text{cm}^2
\]
\[
wh = 4 \times 3 = 12 \, \text{cm}^2
\]

Next, sum these values:
\[
lw + lh + wh = 28 + 21 + 12 = 61 \, \text{cm}^2
\]

Finally, multiply by 2 to find the surface area:
\[
A = 2 \times 61 = 122 \, \text{cm}^2
\]

So, the surface area of the rectangular prism is **122 cm²**.

### Summary of Answers:
1. **Volume:** 84 cm³
2. **Surface Area:** 122 cm²

Would you like more details, or do you have any further questions?

Here are five related questions:
1. What is the formula for the diagonal length of a rectangular prism?
2. How would the volume change if the height of the prism was doubled?
3. What is the surface area of a cube with an edge length equal to the width of the given prism?
4. If the rectangular prism was a hollow box with a wall thickness of 0.5 cm, how would you calculate the volume of the material used?
5. How would the surface area be affected if only the length was increased by 2 cm?

**Tip:** Always label the units in your calculations to avoid confusion, especially when working with measurements in geometry.

Calculate the volume and surface area of a rectangular prism with dimensions 7 cm by 4 cm by 3 cm.

Learn how to calculate the volume and surface area of a rectangular prism with dimensions 7 cm x 4 cm x 3 cm. This problem is suitable for students in Grades 6-8, covering essential geometry concepts such as volume and surface area.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation