8 feet Half a sphere with a radius of 8 feet.

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
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Find the volume and surface area of each object, make sure to show all work and include correct units. ** Round the volume and surface area to the nearest tenth. (Round only your final answer). When determining surface area imagine that you can pick up the figures below. Figures are not always drawn to scale.

 

### Geometry Concepts: Understanding Hemispheres

#### Diagram
The image portrays a two-dimensional representation of a hemisphere, which is a three-dimensional shape. The hemisphere is depicted as half of a sphere, and it shows the following features:

- **Radius**: The radius of the hemisphere is labeled as 8 feet.
- **Shape**: The image illustrates a cross-sectional view of the hemisphere. The flat bottom represents the base, while the curved top represents the surface of the hemisphere.

#### Description
3. **Half a sphere with a radius of 8 feet.**
   - This problem involves understanding the properties of a hemisphere. A hemisphere is essentially half of a sphere.
   - The radius of the hemisphere is given as 8 feet. The radius is the distance from the center of the base (flat surface) to any point on the curved surface.
   - To visualize, imagine cutting a sphere exactly in half through its center; each half would be a hemisphere.

This concept is fundamental in geometry and helps in calculating surface areas and volumes for more complex shapes. When dealing with hemispheres, it's important to remember that the formulas for surface area and volume differ slightly from those of a full sphere.

##### Formulas:
- **Volume of a Hemisphere**: \( V = \frac{2}{3} \pi r^3 \)
- **Surface Area of a Hemisphere**: \( SA = 3 \pi r^2 \)

Where \( r \) is the radius, and \( \pi \) is a mathematical constant approximately equal to 3.14159.

Understanding these properties aids in solving real-world problems involving hemispherical shapes, such as domes, bowls, and various other applications in engineering and architecture.
Transcribed Image Text:### Geometry Concepts: Understanding Hemispheres #### Diagram The image portrays a two-dimensional representation of a hemisphere, which is a three-dimensional shape. The hemisphere is depicted as half of a sphere, and it shows the following features: - **Radius**: The radius of the hemisphere is labeled as 8 feet. - **Shape**: The image illustrates a cross-sectional view of the hemisphere. The flat bottom represents the base, while the curved top represents the surface of the hemisphere. #### Description 3. **Half a sphere with a radius of 8 feet.** - This problem involves understanding the properties of a hemisphere. A hemisphere is essentially half of a sphere. - The radius of the hemisphere is given as 8 feet. The radius is the distance from the center of the base (flat surface) to any point on the curved surface. - To visualize, imagine cutting a sphere exactly in half through its center; each half would be a hemisphere. This concept is fundamental in geometry and helps in calculating surface areas and volumes for more complex shapes. When dealing with hemispheres, it's important to remember that the formulas for surface area and volume differ slightly from those of a full sphere. ##### Formulas: - **Volume of a Hemisphere**: \( V = \frac{2}{3} \pi r^3 \) - **Surface Area of a Hemisphere**: \( SA = 3 \pi r^2 \) Where \( r \) is the radius, and \( \pi \) is a mathematical constant approximately equal to 3.14159. Understanding these properties aids in solving real-world problems involving hemispherical shapes, such as domes, bowls, and various other applications in engineering and architecture.
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