Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Concept explainers
Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.
Question
What is the volume of the cone?
![## SWYK: Volume of Cones
### Problem Statement:
**Given a cone with a height of 6 cm and a base diameter of 6 cm, what is the volume of the cone?**
Use 3.24 for \(\pi\).
### Multiple Choice Options:
- \( 226.08 \, \text{cm}^3 \)
- \( 678.24 \, \text{cm}^3 \)
- \( 565.2 \, \text{cm}^3 \)
- \( 160.56 \, \text{cm}^3 \)
### Notes:
- A calculator is available for use.
### Calculation:
To find the volume of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
1. **Determine the radius:**
The diameter is 6 cm, so the radius \( r \) is half of that, which is
\[ r = \frac{6 \, \text{cm}}{2} = 3 \, \text{cm} \]
2. **Height of the cone:**
Given \( h = 6 \, \text{cm} \)
3. **Insertion into the formula:**
\[ V = \frac{1}{3} \times 3.24 \times (3 \, \text{cm})^2 \times 6 \, \text{cm} \]
\[ V = \frac{1}{3} \times 3.24 \times 9 \, \text{cm}^2 \times 6 \, \text{cm} \]
\[ V = \frac{1}{3} \times 3.24 \times 54 \, \text{cm}^3 \]
\[ V = \frac{1}{3} \times 174.96 \, \text{cm}^3 \]
\[ V = 58.32 \, \text{cm}^3 \]
**None of the provided options match this result, thus it's possible that:
1. There is a keying error in either the problem statement or the provided choices.
2. The given value for \(\pi\) should be reconsidered.
**/](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4eddc7db-750d-4f46-b582-c2598cf45bbc%2Fbc4ac9af-fd5c-49ae-8798-d6b5fe935bb3%2Fkohwt3f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## SWYK: Volume of Cones
### Problem Statement:
**Given a cone with a height of 6 cm and a base diameter of 6 cm, what is the volume of the cone?**
Use 3.24 for \(\pi\).
### Multiple Choice Options:
- \( 226.08 \, \text{cm}^3 \)
- \( 678.24 \, \text{cm}^3 \)
- \( 565.2 \, \text{cm}^3 \)
- \( 160.56 \, \text{cm}^3 \)
### Notes:
- A calculator is available for use.
### Calculation:
To find the volume of a cone, we use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
1. **Determine the radius:**
The diameter is 6 cm, so the radius \( r \) is half of that, which is
\[ r = \frac{6 \, \text{cm}}{2} = 3 \, \text{cm} \]
2. **Height of the cone:**
Given \( h = 6 \, \text{cm} \)
3. **Insertion into the formula:**
\[ V = \frac{1}{3} \times 3.24 \times (3 \, \text{cm})^2 \times 6 \, \text{cm} \]
\[ V = \frac{1}{3} \times 3.24 \times 9 \, \text{cm}^2 \times 6 \, \text{cm} \]
\[ V = \frac{1}{3} \times 3.24 \times 54 \, \text{cm}^3 \]
\[ V = \frac{1}{3} \times 174.96 \, \text{cm}^3 \]
\[ V = 58.32 \, \text{cm}^3 \]
**None of the provided options match this result, thus it's possible that:
1. There is a keying error in either the problem statement or the provided choices.
2. The given value for \(\pi\) should be reconsidered.
**/
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