Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![### Surface Area of Composite Figures
#### Problem:
Find the surface area of the composite figure.
#### Measurements:
- **Cylinder:**
- Radius: \(4\) inches (since the diameter is given as \(8\) inches)
- Height: \(9\) inches
- **Rectangular Prism:**
- Length: \(16\) inches
- Width: \(11\) inches
- Height: \(11\) inches
#### Surface Area Formula for a Cylinder:
\[ SA \text{ of a cylinder} = 2\pi r^2 + 2\pi rh \text{ (Use } 3.14 \text{ for } \pi) \]
#### Instructions:
Include the base of the blue rectangular prism in your answer. Remember to subtract out the bottom of the cylinder and the part of the rectangular prism that it covers.
#### Hint:
Area of a Circle \( A = \pi r^2 \)
---
The composite figure consists of a cylinder placed on top of a rectangular prism.
1. **Calculate the Surface Area of the Cylinder** (excluding the bottom base that touches the rectangular prism):
- Lateral surface area of the cylinder: \( 2\pi rh \)
- Top surface area of the cylinder: \( \pi r^2 \)
- Bottom surface area (base) of the cylinder is not needed since it is covered by the rectangular prism.
2. **Calculate the Surface Area of the Rectangular Prism** (excluding the top area covered by the cylinder's base):
- The sum of the areas of all six faces, but subtract the area of the circle (base of the cylinder) from the top face.
3. **Combine the Surface Areas**:
- Add the lateral surface area of the cylinder and the visible top base.
- Add the modified surface area of the rectangular prism.
These calculations will give you the total surface area of the composite figure.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c3da3a8-213d-4d7e-8e7b-688cde8d89a8%2Ffcfab5af-c227-4fd2-9883-b93c98edccdf%2F6l8fpkd.jpeg&w=3840&q=75)
Transcribed Image Text:### Surface Area of Composite Figures
#### Problem:
Find the surface area of the composite figure.
#### Measurements:
- **Cylinder:**
- Radius: \(4\) inches (since the diameter is given as \(8\) inches)
- Height: \(9\) inches
- **Rectangular Prism:**
- Length: \(16\) inches
- Width: \(11\) inches
- Height: \(11\) inches
#### Surface Area Formula for a Cylinder:
\[ SA \text{ of a cylinder} = 2\pi r^2 + 2\pi rh \text{ (Use } 3.14 \text{ for } \pi) \]
#### Instructions:
Include the base of the blue rectangular prism in your answer. Remember to subtract out the bottom of the cylinder and the part of the rectangular prism that it covers.
#### Hint:
Area of a Circle \( A = \pi r^2 \)
---
The composite figure consists of a cylinder placed on top of a rectangular prism.
1. **Calculate the Surface Area of the Cylinder** (excluding the bottom base that touches the rectangular prism):
- Lateral surface area of the cylinder: \( 2\pi rh \)
- Top surface area of the cylinder: \( \pi r^2 \)
- Bottom surface area (base) of the cylinder is not needed since it is covered by the rectangular prism.
2. **Calculate the Surface Area of the Rectangular Prism** (excluding the top area covered by the cylinder's base):
- The sum of the areas of all six faces, but subtract the area of the circle (base of the cylinder) from the top face.
3. **Combine the Surface Areas**:
- Add the lateral surface area of the cylinder and the visible top base.
- Add the modified surface area of the rectangular prism.
These calculations will give you the total surface area of the composite figure.
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