A steel cylindrical tank must hold 7110 gal of dyed water for a cloth process. Due to space constraints, the cylindrical tank is made 11.0 ft in diameter. How y'all must the tank be? (Water weighs 8.34 lb/gal and 62.4 lb/fr^3.)
A steel cylindrical tank must hold 7110 gal of dyed water for a cloth process. Due to space constraints, the cylindrical tank is made 11.0 ft in diameter. How y'all must the tank be? (Water weighs 8.34 lb/gal and 62.4 lb/fr^3.)
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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A steel cylindrical tank must hold 7110 gal of dyed water for a cloth process. Due to space constraints, the cylindrical tank is made 11.0 ft in diameter.
How y'all must the tank be? (Water weighs 8.34 lb/gal and 62.4 lb/fr^3.)
![### Volume and Capacity Calculations for Cylindrical Tanks
**Volume Calculation:**
To calculate the volume of a cylindrical tank, we use the formula:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder
In the context of the problems presented:
1. **First Problem:**
- Given the volume \( V = 963 \, \text{m}^3 \).
- There's an illustration of a cylindrical tank with a height of \( 17.9 \, \text{m} \).
2. **Second Problem:**
- A steel cylindrical tank needs to hold \( 7110 \, \text{gal} \) of dyed water.
- Due to space constraints, the cylindrical tank has a diameter of \( 11.0 \, \text{ft} \).
Since the diameter is given, the radius \( r \) can be found using:
\[ r = \frac{\text{Diameter}}{2} = \frac{11.0 \, \text{ft}}{2} = 5.5 \, \text{ft} \]
To find the height \( h \) of the tank, we know:
- Water weighs \( 8.34 \, \text{lb/gal} \)
- Water has a density of \( 62.4 \, \text{lb/ft}^3 \)
3. **Third Problem:**
- An oil filter for a small automobile is cylindrical with a radius of \( 1.80 \, \text{in} \) and height \( 3.60 \, \text{in} \).
The volume \( V \) can be calculated using:
\[ V = \pi r^2 h \]
\[ V = \pi (1.80 \, \text{in})^2 (3.60 \, \text{in}) \]
### Diagram Interpretation:
- The first diagram depicts a cylindrical tank with a height labeled as \( 17.9 \, \text{m} \).
### Questions to Answer:
1. **Height of the Steel Cylindrical Tank:**
How tall must the tank be to hold \( 7110 \,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4cf4de5-2539-43da-935f-04d440cecbdb%2Fedee4e42-2394-474f-8cac-6be0345d916b%2Fw8tz9f.jpeg&w=3840&q=75)
Transcribed Image Text:### Volume and Capacity Calculations for Cylindrical Tanks
**Volume Calculation:**
To calculate the volume of a cylindrical tank, we use the formula:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder
In the context of the problems presented:
1. **First Problem:**
- Given the volume \( V = 963 \, \text{m}^3 \).
- There's an illustration of a cylindrical tank with a height of \( 17.9 \, \text{m} \).
2. **Second Problem:**
- A steel cylindrical tank needs to hold \( 7110 \, \text{gal} \) of dyed water.
- Due to space constraints, the cylindrical tank has a diameter of \( 11.0 \, \text{ft} \).
Since the diameter is given, the radius \( r \) can be found using:
\[ r = \frac{\text{Diameter}}{2} = \frac{11.0 \, \text{ft}}{2} = 5.5 \, \text{ft} \]
To find the height \( h \) of the tank, we know:
- Water weighs \( 8.34 \, \text{lb/gal} \)
- Water has a density of \( 62.4 \, \text{lb/ft}^3 \)
3. **Third Problem:**
- An oil filter for a small automobile is cylindrical with a radius of \( 1.80 \, \text{in} \) and height \( 3.60 \, \text{in} \).
The volume \( V \) can be calculated using:
\[ V = \pi r^2 h \]
\[ V = \pi (1.80 \, \text{in})^2 (3.60 \, \text{in}) \]
### Diagram Interpretation:
- The first diagram depicts a cylindrical tank with a height labeled as \( 17.9 \, \text{m} \).
### Questions to Answer:
1. **Height of the Steel Cylindrical Tank:**
How tall must the tank be to hold \( 7110 \,
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