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

Question

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

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