## Geometry Problem Involving a Punch Bowl ### Question 11: A punch bowl is in the shape of a hemisphere. The top rim has a diameter of 37 cm. 1. **Determine the volume of the punch bowl to the nearest cubic centimeter.** 2. **If there are 1000 cubic centimeters in a liter and 3.785 liters in a gallon, determine, to the nearest tenth of a gallon, how much punch can fit in the bowl.** ### Diagram Description: The diagram shows a hemispherical bowl with the top open and the flat circular side facing up. ### Solution Approach: 1. **Calculating the Volume of the Hemisphere:** - Given the diameter \(d = 37\) cm, the radius \(r\) is half the diameter: \[ r = \frac{d}{2} = \frac{37}{2} = 18.5 \, \text{cm} \] - The formula for the volume \(V\) of a hemisphere is: \[ V = \frac{2}{3} \pi r^3 \] - Substituting the radius: \[ V = \frac{2}{3} \pi (18.5)^3 \] - Calculate the volume using the approximate value of \(\pi\): \[ V \approx \frac{2}{3} \times 3.14159 \times 18.5^3 \] 2. **Converting Cubic Centimeters to Liters and Gallons:** - First, convert cubic centimeters to liters: \[ V \, \text{(in liters)} = \frac{V \, \text{(in cubic centimeters)}}{1000} \] - Then, convert liters to gallons since 1 gallon equals 3.785 liters: \[ \text{Volume in gallons} = \frac{V \, \text{(in liters)}}{3.785} \]
## Geometry Problem Involving a Punch Bowl ### Question 11: A punch bowl is in the shape of a hemisphere. The top rim has a diameter of 37 cm. 1. **Determine the volume of the punch bowl to the nearest cubic centimeter.** 2. **If there are 1000 cubic centimeters in a liter and 3.785 liters in a gallon, determine, to the nearest tenth of a gallon, how much punch can fit in the bowl.** ### Diagram Description: The diagram shows a hemispherical bowl with the top open and the flat circular side facing up. ### Solution Approach: 1. **Calculating the Volume of the Hemisphere:** - Given the diameter \(d = 37\) cm, the radius \(r\) is half the diameter: \[ r = \frac{d}{2} = \frac{37}{2} = 18.5 \, \text{cm} \] - The formula for the volume \(V\) of a hemisphere is: \[ V = \frac{2}{3} \pi r^3 \] - Substituting the radius: \[ V = \frac{2}{3} \pi (18.5)^3 \] - Calculate the volume using the approximate value of \(\pi\): \[ V \approx \frac{2}{3} \times 3.14159 \times 18.5^3 \] 2. **Converting Cubic Centimeters to Liters and Gallons:** - First, convert cubic centimeters to liters: \[ V \, \text{(in liters)} = \frac{V \, \text{(in cubic centimeters)}}{1000} \] - Then, convert liters to gallons since 1 gallon equals 3.785 liters: \[ \text{Volume in gallons} = \frac{V \, \text{(in liters)}}{3.785} \]
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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![## Geometry Problem Involving a Punch Bowl
### Question 11:
A punch bowl is in the shape of a hemisphere. The top rim has a diameter of 37 cm.
1. **Determine the volume of the punch bowl to the nearest cubic centimeter.**
2. **If there are 1000 cubic centimeters in a liter and 3.785 liters in a gallon, determine, to the nearest tenth of a gallon, how much punch can fit in the bowl.**
### Diagram Description:
The diagram shows a hemispherical bowl with the top open and the flat circular side facing up.
### Solution Approach:
1. **Calculating the Volume of the Hemisphere:**
- Given the diameter \(d = 37\) cm, the radius \(r\) is half the diameter:
\[
r = \frac{d}{2} = \frac{37}{2} = 18.5 \, \text{cm}
\]
- The formula for the volume \(V\) of a hemisphere is:
\[
V = \frac{2}{3} \pi r^3
\]
- Substituting the radius:
\[
V = \frac{2}{3} \pi (18.5)^3
\]
- Calculate the volume using the approximate value of \(\pi\):
\[
V \approx \frac{2}{3} \times 3.14159 \times 18.5^3
\]
2. **Converting Cubic Centimeters to Liters and Gallons:**
- First, convert cubic centimeters to liters:
\[
V \, \text{(in liters)} = \frac{V \, \text{(in cubic centimeters)}}{1000}
\]
- Then, convert liters to gallons since 1 gallon equals 3.785 liters:
\[
\text{Volume in gallons} = \frac{V \, \text{(in liters)}}{3.785}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9ff93478-fd93-4e87-bf04-0fc4e955b42c%2F26bd23b9-039d-4150-a6bd-da14ef45f4ef%2F0fq7gx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Geometry Problem Involving a Punch Bowl
### Question 11:
A punch bowl is in the shape of a hemisphere. The top rim has a diameter of 37 cm.
1. **Determine the volume of the punch bowl to the nearest cubic centimeter.**
2. **If there are 1000 cubic centimeters in a liter and 3.785 liters in a gallon, determine, to the nearest tenth of a gallon, how much punch can fit in the bowl.**
### Diagram Description:
The diagram shows a hemispherical bowl with the top open and the flat circular side facing up.
### Solution Approach:
1. **Calculating the Volume of the Hemisphere:**
- Given the diameter \(d = 37\) cm, the radius \(r\) is half the diameter:
\[
r = \frac{d}{2} = \frac{37}{2} = 18.5 \, \text{cm}
\]
- The formula for the volume \(V\) of a hemisphere is:
\[
V = \frac{2}{3} \pi r^3
\]
- Substituting the radius:
\[
V = \frac{2}{3} \pi (18.5)^3
\]
- Calculate the volume using the approximate value of \(\pi\):
\[
V \approx \frac{2}{3} \times 3.14159 \times 18.5^3
\]
2. **Converting Cubic Centimeters to Liters and Gallons:**
- First, convert cubic centimeters to liters:
\[
V \, \text{(in liters)} = \frac{V \, \text{(in cubic centimeters)}}{1000}
\]
- Then, convert liters to gallons since 1 gallon equals 3.785 liters:
\[
\text{Volume in gallons} = \frac{V \, \text{(in liters)}}{3.785}
\]
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