Question

PART B:
#8-#10
Find Surface area and Volume of the following 3D shapes. Show all your work. length = 10 width = 6 and hight = 4







8.)


A.) Arrange the steps for finding Surface Area (3 points) and solve (2 points):
Step 1: Find area of each face
Step 2: Add up areas from each face

SOLVE:



Surface Area =__________


B.) Arrange the steps for finding Volume (3 points) and solve (2 points):
Step 1: Find area of the base
Step 2: Multiply area of base (B) to height

SOLVE:



Volume =__________

Answer 1

To find the surface area and volume of a rectangular prism (also known as a cuboid), we can follow the steps outlined in your prompt.

**Given Dimensions:**
- Length (l) = 10
- Width (w) = 6
- Height (h) = 4

### 8A.) Surface Area

#### Arrange the Steps for Finding Surface Area
1. **Step 1**: Find the area of each face.
2. **Step 2**: Add up the areas from each face.

#### Solve:

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

Calculating the areas of each pair of faces:
1. Area of the front and back faces \( (l \times h) \):
- \( 2(l \times h) = 2(10 \times 4) = 2(40) = 80 \)

2. Area of the left and right faces \( (w \times h) \):
- \( 2(w \times h) = 2(6 \times 4) = 2(24) = 48 \)

3. Area of the top and bottom faces \( (l \times w) \):
- \( 2(l \times w) = 2(10 \times 6) = 2(60) = 120 \)

Now, adding all the areas together:
\[
SA = 80 + 48 + 120 = 248
\]

Thus, the Surface Area is:
\[
\text{Surface Area} = 248 \, \text{square units}
\]

---

### 8B.) Volume

#### Arrange the Steps for Finding Volume
1. **Step 1**: Find the area of the base.
2. **Step 2**: Multiply the area of the base (B) by the height.

#### Solve:

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

Calculating the volume:
\[
V = 10 \times 6 \times 4
\]
First, calculate the area of the base (which is \( l \times w \)):
\[
\text{Base Area} = 10 \times 6 = 60
\]

Now, multiply by the height:
\[
V = 60 \times 4 = 240
\]

Thus, the Volume is:
\[
\text{Volume} = 240 \, \text{cubic units}
\]

### Final Answers
- **Surface Area** = 248 square units
- **Volume** = 240 cubic units