Question

1. Explain how to find the Volume of the rectangular prism above. Show all steps! (2 points)

2. Explain how to find the Surface Area of the rectangular prism above. Show all steps! (2 points)

(4 points)
the h is 3.5 in
the l is 5in
and the w is 5 in

Answer 1

To find both the volume and the surface area of a rectangular prism, you can follow these steps:

### 1. Finding the Volume of the Rectangular Prism

The formula to find the volume \( V \) of a rectangular prism is:
\[
V = l \times w \times h
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

**Given:**
- Height \( h = 3.5 \) inches
- Length \( l = 5 \) inches
- Width \( w = 5 \) inches

**Steps:**
1. Substitute the values into the formula:
\[
V = 5 \, \text{in} \times 5 \, \text{in} \times 3.5 \, \text{in}
\]

2. Multiply the length and width first:
\[
5 \times 5 = 25 \, \text{in}^2
\]

3. Now multiply the result by the height:
\[
25 \, \text{in}^2 \times 3.5 \, \text{in} = 87.5 \, \text{in}^3
\]

**Conclusion:**
The volume of the rectangular prism is \( 87.5 \, \text{in}^3 \).

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

The formula to find the surface area \( SA \) of a rectangular prism is:
\[
SA = 2(lw + lh + wh)
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

**Given:**
- Height \( h = 3.5 \) inches
- Length \( l = 5 \) inches
- Width \( w = 5 \) inches

**Steps:**
1. Calculate the area of each pair of faces:
- \( lw = 5 \times 5 = 25 \, \text{in}^2 \)
- \( lh = 5 \times 3.5 = 17.5 \, \text{in}^2 \)
- \( wh = 5 \times 3.5 = 17.5 \, \text{in}^2 \)

2. Now, add these three areas together:
\[
lw + lh + wh = 25 \, \text{in}^2 + 17.5 \, \text{in}^2 + 17.5 \, \text{in}^2
\]
\[
25 + 17.5 + 17.5 = 60 \, \text{in}^2
\]

3. Finally, multiply the result by 2 to get the total surface area:
\[
SA = 2 \times 60 \, \text{in}^2 = 120 \, \text{in}^2
\]

**Conclusion:**
The surface area of the rectangular prism is \( 120 \, \text{in}^2 \).