Question
A.) Arrange the steps for finding Surface Area (3 points) and solve (2 points): diameter = 6 and hight
equals 9
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 =__________
Answers
Answered by
GPT-4o mini
Sure! Let's start by solving Part A and Part B step by step.
### A.) Surface Area
**Step Arrangement:**
1. Step 1: Find area of each face
2. Step 2: Add up areas from each face
For a cylinder, the total surface area (SA) can be calculated using the formula:
\[
SA = 2\pi r^2 + 2\pi rh
\]
where \(r\) is the radius and \(h\) is the height. Given that the diameter is 6, the radius \(r\) will be:
\[
r = \frac{diameter}{2} = \frac{6}{2} = 3
\]
The height \(h\) is given as 9.
**Substituting values:**
1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2\pi (3^2) = 2\pi \cdot 9 = 18\pi
\]
2. Calculate the lateral surface area:
\[
2\pi rh = 2\pi \cdot 3 \cdot 9 = 54\pi
\]
3. Combine the areas:
\[
SA = 18\pi + 54\pi = 72\pi
\]
**Solve:**
Using \( \pi \approx 3.14 \):
\[
SA \approx 72 \cdot 3.14 \approx 226.08
\]
\[
\text{Surface Area} = 72\pi \text{ or } 226.08 \text{ square units}
\]
### B.) Volume
**Step Arrangement:**
1. Step 1: Find area of the base
2. Step 2: Multiply area of base (B) to height
The volume (V) of a cylinder can be calculated using the formula:
\[
V = B \cdot h
\]
where \(B = \pi r^2\) (area of the base) and \(h\) is the height.
**Substituting values:**
1. Calculate the area of the base:
\[
B = \pi r^2 = \pi (3^2) = 9\pi
\]
2. Multiply by height:
\[
V = 9\pi \cdot 9 = 81\pi
\]
**Solve:**
Using \( \pi \approx 3.14 \):
\[
V \approx 81 \cdot 3.14 \approx 254.34
\]
\[
\text{Volume} = 81\pi \text{ or } 254.34 \text{ cubic units}
\]
### Summary:
- **Surface Area =** \(72\pi\) or approximately \(226.08\) square units.
- **Volume =** \(81\pi\) or approximately \(254.34\) cubic units.
### A.) Surface Area
**Step Arrangement:**
1. Step 1: Find area of each face
2. Step 2: Add up areas from each face
For a cylinder, the total surface area (SA) can be calculated using the formula:
\[
SA = 2\pi r^2 + 2\pi rh
\]
where \(r\) is the radius and \(h\) is the height. Given that the diameter is 6, the radius \(r\) will be:
\[
r = \frac{diameter}{2} = \frac{6}{2} = 3
\]
The height \(h\) is given as 9.
**Substituting values:**
1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2\pi (3^2) = 2\pi \cdot 9 = 18\pi
\]
2. Calculate the lateral surface area:
\[
2\pi rh = 2\pi \cdot 3 \cdot 9 = 54\pi
\]
3. Combine the areas:
\[
SA = 18\pi + 54\pi = 72\pi
\]
**Solve:**
Using \( \pi \approx 3.14 \):
\[
SA \approx 72 \cdot 3.14 \approx 226.08
\]
\[
\text{Surface Area} = 72\pi \text{ or } 226.08 \text{ square units}
\]
### B.) Volume
**Step Arrangement:**
1. Step 1: Find area of the base
2. Step 2: Multiply area of base (B) to height
The volume (V) of a cylinder can be calculated using the formula:
\[
V = B \cdot h
\]
where \(B = \pi r^2\) (area of the base) and \(h\) is the height.
**Substituting values:**
1. Calculate the area of the base:
\[
B = \pi r^2 = \pi (3^2) = 9\pi
\]
2. Multiply by height:
\[
V = 9\pi \cdot 9 = 81\pi
\]
**Solve:**
Using \( \pi \approx 3.14 \):
\[
V \approx 81 \cdot 3.14 \approx 254.34
\]
\[
\text{Volume} = 81\pi \text{ or } 254.34 \text{ cubic units}
\]
### Summary:
- **Surface Area =** \(72\pi\) or approximately \(226.08\) square units.
- **Volume =** \(81\pi\) or approximately \(254.34\) cubic units.