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
Related questions
Question
![### Geometry - Spatial Reasoning Assignment
**Topic: Calculating Volumes of Composite Figures**
#### Homework Question:
**Question 12 of 19:**
Find the volume of the composite figure. Round the answer to the nearest tenth.
The figure consists of a rectangular prism with a semicircular cylinder (half-cylinder) attached to one of its faces. The dimensions of the rectangular prism are:
- Length: 11 cm
- Width: 4 cm
- Height: 5 cm
The dimensions of the semicircular cylinder are:
- Radius of the cylinder's base: 2 cm
- Height of the cylinder: 4 cm (same as the width of the rectangular prism)
### Calculation Steps:
1. **Volume of the Rectangular Prism:**
\[
V_{\text{Rectangular Prism}} = \text{Length} \times \text{Width} \times \text{Height}
\]
\[
V_{\text{Rectangular Prism}} = 11 \, \text{cm} \times 4 \, \text{cm} \times 5 \, \text{cm} = 220 \, \text{cm}^3
\]
2. **Volume of the Semicircular Cylinder:**
The volume of a full cylinder is given by:
\[
V_{\text{Cylinder}} = \pi \times r^2 \times h
\]
Since we have a semicircular cylinder:
\[
V_{\text{Semicircular Cylinder}} = \frac{1}{2} \times \pi \times r^2 \times h
\]
\[
V_{\text{Semicircular Cylinder}} = \frac{1}{2} \times \pi \times (2 \, \text{cm})^2 \times 4 \, \text{cm}
\]
\[
V_{\text{Semicircular Cylinder}} = \frac{1}{2} \times \pi \times 4 \times 4
\]
\[
V_{\text{Semicircular Cylinder}} = 8\pi \, \text{cm}^3 \approx 25.1 \, \text{cm}^3
\]
3. **Total Volume of the Composite Figure:**
The total volume is the sum of the volumes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9bcd254-903f-482d-922c-1ecef4183c9a%2Fb65b1182-d9d6-4302-88da-8f9e27a1c53c%2Fo4fqck2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry - Spatial Reasoning Assignment
**Topic: Calculating Volumes of Composite Figures**
#### Homework Question:
**Question 12 of 19:**
Find the volume of the composite figure. Round the answer to the nearest tenth.
The figure consists of a rectangular prism with a semicircular cylinder (half-cylinder) attached to one of its faces. The dimensions of the rectangular prism are:
- Length: 11 cm
- Width: 4 cm
- Height: 5 cm
The dimensions of the semicircular cylinder are:
- Radius of the cylinder's base: 2 cm
- Height of the cylinder: 4 cm (same as the width of the rectangular prism)
### Calculation Steps:
1. **Volume of the Rectangular Prism:**
\[
V_{\text{Rectangular Prism}} = \text{Length} \times \text{Width} \times \text{Height}
\]
\[
V_{\text{Rectangular Prism}} = 11 \, \text{cm} \times 4 \, \text{cm} \times 5 \, \text{cm} = 220 \, \text{cm}^3
\]
2. **Volume of the Semicircular Cylinder:**
The volume of a full cylinder is given by:
\[
V_{\text{Cylinder}} = \pi \times r^2 \times h
\]
Since we have a semicircular cylinder:
\[
V_{\text{Semicircular Cylinder}} = \frac{1}{2} \times \pi \times r^2 \times h
\]
\[
V_{\text{Semicircular Cylinder}} = \frac{1}{2} \times \pi \times (2 \, \text{cm})^2 \times 4 \, \text{cm}
\]
\[
V_{\text{Semicircular Cylinder}} = \frac{1}{2} \times \pi \times 4 \times 4
\]
\[
V_{\text{Semicircular Cylinder}} = 8\pi \, \text{cm}^3 \approx 25.1 \, \text{cm}^3
\]
3. **Total Volume of the Composite Figure:**
The total volume is the sum of the volumes
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