Question

Find the volume and the surface area of the solid.
2 in
6 in
4 in
Question content area bottom
Part 1
The volume is
  
enter your response here
▼
inches
square inches
cubic inches
. ​(Simplify your​ answer.)

Answer 1

To find the volume and the surface area of a rectangular prism with dimensions 2 inches, 6 inches, and 4 inches, we can use the following formulas:

**Volume (V)** of a rectangular prism is calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

**Surface Area (SA)** of a rectangular prism is calculated using the formula:
\[
SA = 2 \times (\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length})
\]

### Step 1: Volume Calculation
Using the dimensions:
- Length = 6 in
- Width = 4 in
- Height = 2 in

\[
V = 6 \times 4 \times 2
\]
\[
V = 48 \text{ cubic inches}
\]

### Step 2: Surface Area Calculation
Using the same dimensions, we calculate the surface area:
\[
SA = 2 \times (6 \times 4 + 4 \times 2 + 2 \times 6)
\]
Calculating each term:
- \(6 \times 4 = 24\)
- \(4 \times 2 = 8\)
- \(2 \times 6 = 12\)

Now plug those into the formula:
\[
SA = 2 \times (24 + 8 + 12) = 2 \times 44 = 88 \text{ square inches}
\]

### Final Answers
- Volume: **48 cubic inches**
- Surface Area: **88 square inches**

So, the volume is \(48\) cubic inches.