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
Related questions
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
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## Calculating the Volume of a Cone
In this exercise, you are tasked with finding the volume of a cone. The question is displayed on the screen of the Personal Math Trainer software.
### Problem Statement
Find the volume of the cone. Round the answer to the nearest tenth.
### Given Measurements
- **Radius (r)**: 1.9 mm
- **Height (h)**: 4.5 mm
### Diagram Description
The diagram provided shows a cone with the following details:
- A vertical dashed line represents the height, labeled as 4.5 mm.
- A horizontal dashed line within the circular base indicates the radius, labeled as 1.9 mm.
### Volume Formula
The volume \( V \) of a cone can be calculated using the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( \pi \) is a constant (pi), approximately 3.14159.
- \( r \) is the radius of the cone's base.
- \( h \) is the height of the cone.
### Calculate the Volume
1. Plug the values into the formula:
\[ V = \frac{1}{3} \pi (1.9)^2 (4.5) \]
2. Calculate the squared radius:
\[ (1.9)^2 = 3.61 \]
3. Multiply by the height:
\[ 3.61 \times 4.5 = 16.245 \]
4. Multiply by \(\frac{1}{3} \pi \):
\[ V = \frac{1}{3} \times 3.14159 \times 16.245 \approx 16.959 \]
So, the volume of the cone is approximately 16.959 mm³.
### Final Answer
Round to the nearest tenth:
\[ V \approx 17.0 \, \text{mm}^3 \]
Be sure to input your final answer into the provided answer box in the Personal Math Trainer interface.
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### Interface Buttons
- **Check Answer**: Click this button to verify if your calculated volume is correct.
- **Next**: Click this button to proceed to the next question in the set.
### Progress
This is Question 9 out of 19 in your current exercise set.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd981abda-0735-44a1-b3a7-87e085a24ba8%2F64ab00f6-8f9e-48aa-8dda-d87ea37707e9%2Fewmt00v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
## Calculating the Volume of a Cone
In this exercise, you are tasked with finding the volume of a cone. The question is displayed on the screen of the Personal Math Trainer software.
### Problem Statement
Find the volume of the cone. Round the answer to the nearest tenth.
### Given Measurements
- **Radius (r)**: 1.9 mm
- **Height (h)**: 4.5 mm
### Diagram Description
The diagram provided shows a cone with the following details:
- A vertical dashed line represents the height, labeled as 4.5 mm.
- A horizontal dashed line within the circular base indicates the radius, labeled as 1.9 mm.
### Volume Formula
The volume \( V \) of a cone can be calculated using the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( \pi \) is a constant (pi), approximately 3.14159.
- \( r \) is the radius of the cone's base.
- \( h \) is the height of the cone.
### Calculate the Volume
1. Plug the values into the formula:
\[ V = \frac{1}{3} \pi (1.9)^2 (4.5) \]
2. Calculate the squared radius:
\[ (1.9)^2 = 3.61 \]
3. Multiply by the height:
\[ 3.61 \times 4.5 = 16.245 \]
4. Multiply by \(\frac{1}{3} \pi \):
\[ V = \frac{1}{3} \times 3.14159 \times 16.245 \approx 16.959 \]
So, the volume of the cone is approximately 16.959 mm³.
### Final Answer
Round to the nearest tenth:
\[ V \approx 17.0 \, \text{mm}^3 \]
Be sure to input your final answer into the provided answer box in the Personal Math Trainer interface.
---
### Interface Buttons
- **Check Answer**: Click this button to verify if your calculated volume is correct.
- **Next**: Click this button to proceed to the next question in the set.
### Progress
This is Question 9 out of 19 in your current exercise set.
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