https://file.aiquickdraw.com/mathbot/file/1727316381693b4dfdsve.jpg

The question in the image asks to find both the volume and surface area of a rectangular prism (box). The dimensions of the box are provided:

- Length: 6 inches
- Width: 4 inches
- Height: 3.5 inches

### (a) Volume
The formula for the volume \( V \) of a rectangular prism is:

\[
V = \text{length} \times \text{width} \times \text{height}
\]

Substitute the given dimensions:

\[
V = 6 \, \text{in} \times 4 \, \text{in} \times 3.5 \, \text{in} = 84 \, \text{in}^3
\]

So, the volume is **84 cubic inches**.

### (b) Surface Area
The formula for the surface area \( A \) of a rectangular prism is:

\[
A = 2 \times (\text{length} \times \text{width} + \text{length} \times \text{height} + \text{width} \times \text{height})
\]

Substitute the given dimensions:

\[
A = 2 \times (6 \times 4 + 6 \times 3.5 + 4 \times 3.5)
\]

First, calculate each product:

- \( 6 \times 4 = 24 \)
- \( 6 \times 3.5 = 21 \)
- \( 4 \times 3.5 = 14 \)

Now, sum them:

\[
24 + 21 + 14 = 59
\]

Finally, multiply by 2:

\[
A = 2 \times 59 = 118 \, \text{in}^2
\]

So, the surface area is **118 square inches**.

---

Would you like more details on any step or have any questions? Here are 5 related questions:

1. How is the formula for surface area of a rectangular prism derived?
2. How would the volume change if one of the dimensions was doubled?
3. What is the lateral surface area of this rectangular prism?
4. How can the surface area formula be applied to irregular shapes?
5. How does surface area-to-volume ratio affect physical properties like heat retention?

**Tip:** Understanding how to apply basic formulas for 3D shapes (like volume and surface area) is crucial in geometry and real-world applications such as engineering and architecture.

Find (a) the volume and (b) the surface area of a rectangular prism with dimensions: length = 6 inches, width = 4 inches, height = 3.5 inches.

Calculate the volume and surface area of a rectangular prism with dimensions: length = 6 inches, width = 4 inches, and height = 3.5 inches. Learn step-by-step methods, including formulas and theorems, for solving these geometric problems. Ideal for students in Grades 6-8.

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