https://file.aiquickdraw.com/mathbot/file/1727341280467y2o19o86.jpg

To solve this problem, we will find the **surface area** and **volume** of the rectangular prism shown in the image.

The dimensions of the prism are:
- Length (\(l\)) = 7 cm
- Width (\(w\)) = 5 cm
- Height (\(h\)) = 2 cm

### a. Surface Area
The surface area (\(SA\)) of a rectangular prism is calculated using the formula:
\[
SA = 2lw + 2lh + 2wh
\]

Substituting the given values:
\[
SA = 2(7)(5) + 2(7)(2) + 2(5)(2)
\]
\[
SA = 2(35) + 2(14) + 2(10)
\]
\[
SA = 70 + 28 + 20 = 118 \, \text{cm}^2
\]

### b. Volume
The volume (\(V\)) of a rectangular prism is calculated using the formula:
\[
V = l \times w \times h
\]

Substituting the given values:
\[
V = 7 \times 5 \times 2 = 70 \, \text{cm}^3
\]

### Final Answers:
- **Surface Area** = 118 cm²
- **Volume** = 70 cm³

Let me know if you'd like further clarification!

---

Here are some follow-up questions to practice:
1. What would the surface area be if the height were 4 cm?
2. How does the surface area change if the width is doubled?
3. What is the volume if the length is reduced by half?
4. Calculate the surface area for a cube with side length of 6 cm.
5. If the length is increased by 3 cm, what would be the new volume?

**Tip:** Always remember to include units when calculating area and volume to avoid confusion.

Find the surface area and volume of a rectangular prism with dimensions: length = 7 cm, width = 5 cm, height = 2 cm.

This tutorial explains how to find the surface area and volume of a rectangular prism with a length of 7 cm, width of 5 cm, and height of 2 cm. It covers key geometry concepts and includes detailed calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation