Find the volume of a cone with a base diameter of 6 cm and a height of 11 cm. Write the exact volume in terms of T, and be sure to include the correct unit in your answer. 11 cm 6 ст.
Find the volume of a cone with a base diameter of 6 cm and a height of 11 cm. Write the exact volume in terms of T, and be sure to include the correct unit in your answer. 11 cm 6 ст.
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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**Finding the Volume of a Cone**
***Problem Statement:***
Find the volume of a cone with a base diameter of 6 cm and a height of 11 cm. Write the exact volume in terms of π, and be sure to include the correct unit in your answer.
---
***Diagram Explanation:***
The accompanying diagram depicts a cone with the following measurements:
- Height: 11 cm
- Base Diameter: 6 cm
A vertical dashed line indicates the height of the cone (11 cm) extending from the apex (top) to the center of the base. The base diameter is labeled as 6 cm.
---
***Solution:***
To find the volume of a cone, use the formula:
\[ V = \frac{1}{3}\pi r^2 h \]
First, determine the radius \( r \) of the base of the cone.
- Since the diameter is 6 cm, the radius \( r \) is half of that:
\[ r = \frac{6}{2} = 3 \text{ cm} \]
Using the given measurements:
- Radius \( r \) = 3 cm
- Height \( h \) = 11 cm
Substitute these values into the volume formula:
\[ V = \frac{1}{3}\pi (3)^2 (11)\]
\[ V = \frac{1}{3}\pi (9)(11)\]
\[ V = \frac{1}{3}\pi (99)\]
\[ V = 33\pi \]
Thus, the exact volume of the cone is:
\[ \boxed{33\pi \text{ cm}^3} \]
Make sure to include the correct unit (cubic centimeters) in your answer.
---
***Additional Interactive Elements:***
- The empty box on the right side of the problem allows you to input your answer.
- Below the input box, there are unit buttons to select from. Make sure to select "cm³" (cubic centimeters) when entering the final answer.
- Options are also available to clear the answer (X) or access help (?).
---
**Tip:** Always ensure that your final answer is in terms of π and includes the correct unit for full credit.
---
© 2021 McGraw-Hill Education. All Rights Reserved.
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Transcribed Image Text:---
**Finding the Volume of a Cone**
***Problem Statement:***
Find the volume of a cone with a base diameter of 6 cm and a height of 11 cm. Write the exact volume in terms of π, and be sure to include the correct unit in your answer.
---
***Diagram Explanation:***
The accompanying diagram depicts a cone with the following measurements:
- Height: 11 cm
- Base Diameter: 6 cm
A vertical dashed line indicates the height of the cone (11 cm) extending from the apex (top) to the center of the base. The base diameter is labeled as 6 cm.
---
***Solution:***
To find the volume of a cone, use the formula:
\[ V = \frac{1}{3}\pi r^2 h \]
First, determine the radius \( r \) of the base of the cone.
- Since the diameter is 6 cm, the radius \( r \) is half of that:
\[ r = \frac{6}{2} = 3 \text{ cm} \]
Using the given measurements:
- Radius \( r \) = 3 cm
- Height \( h \) = 11 cm
Substitute these values into the volume formula:
\[ V = \frac{1}{3}\pi (3)^2 (11)\]
\[ V = \frac{1}{3}\pi (9)(11)\]
\[ V = \frac{1}{3}\pi (99)\]
\[ V = 33\pi \]
Thus, the exact volume of the cone is:
\[ \boxed{33\pi \text{ cm}^3} \]
Make sure to include the correct unit (cubic centimeters) in your answer.
---
***Additional Interactive Elements:***
- The empty box on the right side of the problem allows you to input your answer.
- Below the input box, there are unit buttons to select from. Make sure to select "cm³" (cubic centimeters) when entering the final answer.
- Options are also available to clear the answer (X) or access help (?).
---
**Tip:** Always ensure that your final answer is in terms of π and includes the correct unit for full credit.
---
© 2021 McGraw-Hill Education. All Rights Reserved.
---
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