Question

PART B:
#8-#10
Find Surface area and Volume of the following 3D shapes. Show all your work.


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 3D shape, we typically need to specify the shape in question (for example, a cube, rectangular prism, cylinder, etc.). Since no specific shape was given, I will choose a rectangular prism (also known as a cuboid) for the calculations. You can substitute with the appropriate formulas depending on the shape you are analyzing.

### Rectangular Prism Details:
- Length (l) = 4 units
- Width (w) = 3 units
- Height (h) = 5 units

### 8A: Surface Area

**Arrange the steps:**
1. Find the area of each face.
2. Add up areas from each face.

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

Calculating each part:
- Area of two faces with dimensions l and w: \( 2lw = 2(4)(3) = 24 \)
- Area of two faces with dimensions l and h: \( 2lh = 2(4)(5) = 40 \)
- Area of two faces with dimensions w and h: \( 2wh = 2(3)(5) = 30 \)

Now add these areas together:
\[
SA = 24 + 40 + 30 = 94
\]

**Surface Area = 94 square units**

---

### 8B: Volume

**Arrange the steps:**
1. Find area of the base.
2. Multiply the area of base (B) by the height.

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

Calculating:
\[
V = 4 \times 3 \times 5 = 60
\]

**Volume = 60 cubic units**

---

**Summary:**
- Surface Area = 94 square units
- Volume = 60 cubic units

Feel free to specify another shape if needed!