https://file.aiquickdraw.com/mathbot/file/1726543216093ig0hz7w3.jpg

The image shows a rectangular box with dimensions:

- Height: 3 feet
- Length: 12 feet
- Width: 7 feet

The task is to find both the **volume** and the **surface area** of the box.

### Volume of the box:
The volume \( V \) of a rectangular box is given by:
\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]

Substituting the values:
\[
V = 12 \, \text{ft} \times 7 \, \text{ft} \times 3 \, \text{ft} = 252 \, \text{cubic feet}
\]

### Surface Area of the box:
The surface area \( A \) of a rectangular box is calculated by summing the areas of all six faces. The formula is:
\[
A = 2 \times (\text{Length} \times \text{Width} + \text{Width} \times \text{Height} + \text{Length} \times \text{Height})
\]

Substituting the values:
\[
A = 2 \times (12 \, \text{ft} \times 7 \, \text{ft} + 7 \, \text{ft} \times 3 \, \text{ft} + 12 \, \text{ft} \times 3 \, \text{ft})
\]
\[
A = 2 \times (84 \, \text{sq ft} + 21 \, \text{sq ft} + 36 \, \text{sq ft}) = 2 \times 141 \, \text{sq ft} = 282 \, \text{square feet}
\]

### Final Answer:
- Volume: **252 cubic feet**
- Surface Area: **282 square feet**

Do you have any further questions or need more details?

---

Here are 5 related questions:
1. How would the volume change if the height of the box were doubled?
2. What is the effect on the surface area if all dimensions are doubled?
3. How do you find the diagonal of the box?
4. How would you calculate the volume if the box had an open top?
5. What is the formula for surface area if the box is a cube?

**Tip:** Always double-check that the units of all measurements are consistent when calculating volume or surface area.

Use the calculator to find the volume and surface area of the box with dimensions 12 feet by 7 feet by 3 feet.

Calculate the volume and surface area of a rectangular box with dimensions 12 feet by 7 feet by 3 feet. Learn how to use key geometric formulas to solve this real-world math problem, suitable 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