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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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
![### Problem 18: Calculating the Volume of a Hemisphere-Shaped Coffee Cup
**Question:**
What is the volume of a hemisphere-shaped coffee cup if the width of the coffee cup is about 16.51 centimeters? (Use 3.14 for π)
**Visual Aids:**
The question is accompanied by an image of a white coffee cup placed on a matching saucer. Below the question, there are four multiple-choice options for the volume of the hemisphere-shaped coffee cup.
**Options:**
1. 2355.16 cm³
2. 1177.58 cm³
3. 18,841.25 cm³
4. 12,850.80 cm³
**Explanation:**
To find the volume of a hemisphere, you can use the formula:
\[ V = \frac{2}{3} \pi r^3 \]
First, determine the radius of the hemisphere:
The diameter is given as 16.51 cm, so the radius \( r \) is:
\[ r = \frac{16.51}{2} = 8.255 \text{ cm} \]
Using the given value of π (3.14), insert the radius into the volume formula:
\[ V = \frac{2}{3} \times 3.14 \times (8.255)^3 \]
Calculate the cube of the radius:
\[ (8.255)^3 \approx 562.79 \text{ cm}^3 \]
Now multiply by \(\frac{2}{3}\) and π:
\[ V = \frac{2}{3} \times 3.14 \times 562.79 \approx 1177.58 \text{ cm}^3 \]
So, the correct answer is 1177.58 cm³, which corresponds to option 2.
By comprehensively breaking down the calculation steps, we ensure learners understand the process of determining the volume of a hemisphere.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4b71a59-4615-47bf-a686-737fe976edbf%2F8f6523f7-4aa9-484a-b17c-27a761442a09%2Fwaiwmhs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 18: Calculating the Volume of a Hemisphere-Shaped Coffee Cup
**Question:**
What is the volume of a hemisphere-shaped coffee cup if the width of the coffee cup is about 16.51 centimeters? (Use 3.14 for π)
**Visual Aids:**
The question is accompanied by an image of a white coffee cup placed on a matching saucer. Below the question, there are four multiple-choice options for the volume of the hemisphere-shaped coffee cup.
**Options:**
1. 2355.16 cm³
2. 1177.58 cm³
3. 18,841.25 cm³
4. 12,850.80 cm³
**Explanation:**
To find the volume of a hemisphere, you can use the formula:
\[ V = \frac{2}{3} \pi r^3 \]
First, determine the radius of the hemisphere:
The diameter is given as 16.51 cm, so the radius \( r \) is:
\[ r = \frac{16.51}{2} = 8.255 \text{ cm} \]
Using the given value of π (3.14), insert the radius into the volume formula:
\[ V = \frac{2}{3} \times 3.14 \times (8.255)^3 \]
Calculate the cube of the radius:
\[ (8.255)^3 \approx 562.79 \text{ cm}^3 \]
Now multiply by \(\frac{2}{3}\) and π:
\[ V = \frac{2}{3} \times 3.14 \times 562.79 \approx 1177.58 \text{ cm}^3 \]
So, the correct answer is 1177.58 cm³, which corresponds to option 2.
By comprehensively breaking down the calculation steps, we ensure learners understand the process of determining the volume of a hemisphere.
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