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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![The image appears to be a screenshot of an educational website illustrating the formulas for the volumes of various geometric shapes.
### Explanation:
#### Geometric Shapes and Formulas:
1. **Rectangular Prism (illustrated in the top diagram)**
- The volume formula is given by:
\[
A = Bh
\]
- Where \( B \) is the area of the base and \( h \) is the height.
2. **Cone (illustrated in the bottom diagram)**
- The volume formula is given by:
\[
A = \frac{Bh}{3}
\]
- Where \( B \) is the area of the base and \( h \) is the height.
- Alternatively, the volume of a cone can also be expressed in terms of the radius \( r \) of the base and the height \( h \) as:
\[
A = \frac{\pi r^2 h}{3}
\]
3. **Cylinder (not directly illustrated but included in the formulas)**
- The volume formula for a cylinder is:
\[
A = \pi r^2 h
\]
### Summary of Formulas Displayed:
- \( A = Bh \)
- \( A = \frac{Bh}{3} \)
- \( A = \pi r^2 h \)
- \( A = \frac{\pi r^2 h}{3} \)
These formulas define the volumes for different geometric shapes, serving as a quick reference for students learning about geometry.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e046ea4-05f5-4640-8a37-b1c9a5ef5104%2Fa113d86e-8cce-466e-a84a-f4cbe0320379%2Fxuge69s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image appears to be a screenshot of an educational website illustrating the formulas for the volumes of various geometric shapes.
### Explanation:
#### Geometric Shapes and Formulas:
1. **Rectangular Prism (illustrated in the top diagram)**
- The volume formula is given by:
\[
A = Bh
\]
- Where \( B \) is the area of the base and \( h \) is the height.
2. **Cone (illustrated in the bottom diagram)**
- The volume formula is given by:
\[
A = \frac{Bh}{3}
\]
- Where \( B \) is the area of the base and \( h \) is the height.
- Alternatively, the volume of a cone can also be expressed in terms of the radius \( r \) of the base and the height \( h \) as:
\[
A = \frac{\pi r^2 h}{3}
\]
3. **Cylinder (not directly illustrated but included in the formulas)**
- The volume formula for a cylinder is:
\[
A = \pi r^2 h
\]
### Summary of Formulas Displayed:
- \( A = Bh \)
- \( A = \frac{Bh}{3} \)
- \( A = \pi r^2 h \)
- \( A = \frac{\pi r^2 h}{3} \)
These formulas define the volumes for different geometric shapes, serving as a quick reference for students learning about geometry.

Transcribed Image Text:The image displays four different three-dimensional geometrical shapes along with empty labels to the right of each shape. Here is a detailed description of each shape from top to bottom:
1. **Pyramid:**
- **Description:** This shape is a three-dimensional polyhedron with a polygonal base and triangular faces that converge at a single point called the apex.
2. **Ellipsoid:**
- **Description:** This shape is a three-dimensional surface, which resembles a stretched or squished sphere. It looks similar to an ellipse rotated about one of its principal axes.
3. **Cube:**
- **Description:** This shape is a three-dimensional figure with six equal square faces. Each face meets another at a right angle, and all the edges and vertices are the same.
4. **Cone:**
- **Description:** This shape is a three-dimensional figure with a circular base and a single vertex. It tapers smoothly from the base to the vertex.
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