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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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
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how do i find the lateral height
![**Calculating the Surface Area of a Right Circular Cone**
This educational resource explains how to calculate the surface area of a right circular cone given its dimensions.
### Diagram Explanation:
The diagram provided represents a right circular cone with the following dimensions:
- The height (h) of the cone is 4 inches.
- The radius (r) of the base of the cone is 6 inches.
### Steps to Calculate the Surface Area:
The surface area of a right circular cone consists of two parts:
1. **Lateral Surface Area (LSA)**: The area of the cone's slanted surface.
2. **Base Surface Area (BSA)**: The area of the cone's circular base.
#### 1. Lateral Surface Area (LSA):
To calculate the Lateral Surface Area, we use the formula:
\[ \text{LSA} = \pi r l \]
where \( l \) is the slant height of the cone.
To find the slant height \( l \), we use the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} \]
Substituting the given dimensions:
\[ l = \sqrt{6^2 + 4^2} \]
\[ l = \sqrt{36 + 16} \]
\[ l = \sqrt{52} \]
\[ l \approx 7.21 \, \text{inches} \]
Now, calculating the LSA:
\[ \text{LSA} = \pi \cdot 6 \cdot 7.21 \]
\[ \text{LSA} \approx 135.78 \, \text{in}^2 \]
#### 2. Base Surface Area (BSA):
To calculate the Base Surface Area, we use the formula:
\[ \text{BSA} = \pi r^2 \]
Substituting the given dimensions:
\[ \text{BSA} = \pi \cdot 6^2 \]
\[ \text{BSA} = \pi \cdot 36 \]
\[ \text{BSA} \approx 113.1 \, \text{in}^2 \]
### Total Surface Area (TSA):
The total surface area of the cone is the sum of the lateral and base surface areas:
\[ \text{TSA} = \text{LSA} + \text{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3270e33a-773c-4d59-a44c-8e0b9afaafb6%2Fd54cfacb-f911-4883-96f8-05017b5f7284%2F0g6rzzzr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculating the Surface Area of a Right Circular Cone**
This educational resource explains how to calculate the surface area of a right circular cone given its dimensions.
### Diagram Explanation:
The diagram provided represents a right circular cone with the following dimensions:
- The height (h) of the cone is 4 inches.
- The radius (r) of the base of the cone is 6 inches.
### Steps to Calculate the Surface Area:
The surface area of a right circular cone consists of two parts:
1. **Lateral Surface Area (LSA)**: The area of the cone's slanted surface.
2. **Base Surface Area (BSA)**: The area of the cone's circular base.
#### 1. Lateral Surface Area (LSA):
To calculate the Lateral Surface Area, we use the formula:
\[ \text{LSA} = \pi r l \]
where \( l \) is the slant height of the cone.
To find the slant height \( l \), we use the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} \]
Substituting the given dimensions:
\[ l = \sqrt{6^2 + 4^2} \]
\[ l = \sqrt{36 + 16} \]
\[ l = \sqrt{52} \]
\[ l \approx 7.21 \, \text{inches} \]
Now, calculating the LSA:
\[ \text{LSA} = \pi \cdot 6 \cdot 7.21 \]
\[ \text{LSA} \approx 135.78 \, \text{in}^2 \]
#### 2. Base Surface Area (BSA):
To calculate the Base Surface Area, we use the formula:
\[ \text{BSA} = \pi r^2 \]
Substituting the given dimensions:
\[ \text{BSA} = \pi \cdot 6^2 \]
\[ \text{BSA} = \pi \cdot 36 \]
\[ \text{BSA} \approx 113.1 \, \text{in}^2 \]
### Total Surface Area (TSA):
The total surface area of the cone is the sum of the lateral and base surface areas:
\[ \text{TSA} = \text{LSA} + \text{
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