Question

A.) Arrange the steps for finding Surface Area (3 points) and solve (2 points): the cylinder has a hight of 9 and diameter os 6


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

### A.) Finding Surface Area of a Cylinder

**Steps:**
1. Step 1: Find area of each face
2. Step 2: Add up areas from each face

**Surface Area Calculation:**

To find the surface area \( S \) of a cylinder, we use the formula:

\[
S = 2\pi r^2 + 2\pi rh
\]

where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

**Given:**
- Height \( h = 9 \)
- Diameter = 6, therefore radius \( r = \frac{6}{2} = 3 \)

1. Calculate the area of the two circular bases:
\[
\text{Area of bases} = 2\pi r^2 = 2\pi (3)^2 = 2\pi (9) = 18\pi
\]

2. Calculate the lateral surface area:
\[
\text{Lateral surface area} = 2\pi rh = 2\pi (3)(9) = 54\pi
\]

3. Add the areas together:
\[
S = 18\pi + 54\pi = 72\pi
\]

**Final Surface Area:**

\[
\text{Surface Area} \approx 72 \times 3.14 \approx 226.08
\]

So,
\[
\text{Surface Area} = 72\pi \text{ or approximately } 226.08
\]

---

### B.) Finding Volume of a Cylinder

**Steps:**
1. Step 1: Find area of the base
2. Step 2: Multiply area of base (B) to height

**Volume Calculation:**

To find the volume \( V \) of a cylinder, we use the formula:

\[
V = B \times h
\]

where \( B \) is the area of the base.

1. Calculate the area of the base:
\[
B = \pi r^2 = \pi (3)^2 = 9\pi
\]

2. Multiply the area of the base by the height:
\[
V = B \times h = 9\pi \times 9 = 81\pi
\]

**Final Volume:**

\[
\text{Volume} \approx 81 \times 3.14 \approx 254.34
\]

So,
\[
\text{Volume} = 81\pi \text{ or approximately } 254.34
\]