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Answer :
Sure, let's go through how to solve each part of the problem step-by-step.
### Volume of Cylinders
The volume [tex]\( V \)[/tex] of a cylinder can be calculated using the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylinder.
#### Part A:
- Given: [tex]\( r = 12 \)[/tex] inches, [tex]\( h = 4 \)[/tex] inches
- Calculation:
[tex]\[ V = \pi \times 12^2 \times 4 \][/tex]
[tex]\[ V \approx 1809.6 \, \text{cubic inches} \][/tex]
#### Part B:
- Given: [tex]\( r = 6 \)[/tex] feet, height uses the result from Part A as [tex]\( h = 1809.6 \)[/tex]
- Calculation:
[tex]\[ V = \pi \times 6^2 \times 1809.6 \][/tex]
[tex]\[ V = 204660.9 \, \text{cubic feet} \][/tex]
#### Part C:
- Given: [tex]\( r = 3 \)[/tex] cm, [tex]\( h = 13 \)[/tex] cm
- Calculation:
[tex]\[ V = \pi \times 3^2 \times 13 \][/tex]
[tex]\[ V \approx 367.6 \, \text{cubic centimeters} \][/tex]
#### Part D:
- Given: [tex]\( r = 9 \)[/tex] m, [tex]\( h = 11 \)[/tex] m
- Calculation:
[tex]\[ V = \pi \times 9^2 \times 11 \][/tex]
[tex]\[ V \approx 2799.2 \, \text{cubic meters} \][/tex]
#### Part E:
- Given: [tex]\( r = 8 \)[/tex] ft, [tex]\( h = 15 \)[/tex] ft
- Calculation:
[tex]\[ V = \pi \times 8^2 \times 15 \][/tex]
[tex]\[ V \approx 3015.9 \, \text{cubic feet} \][/tex]
#### Part F:
- Given: [tex]\( d = 10 \)[/tex] cm, [tex]\( h = 7 \)[/tex] cm
- Calculate radius [tex]\( r = \frac{d}{2} = 5 \)[/tex] cm
- Calculation:
[tex]\[ V = \pi \times 5^2 \times 7 \][/tex]
[tex]\[ V \approx 549.8 \, \text{cubic centimeters} \][/tex]
#### Part G:
- Given: [tex]\( d = 3 \)[/tex] cm, [tex]\( h = 9 \)[/tex] cm
- Calculate radius [tex]\( r = \frac{d}{2} = 1.5 \)[/tex] cm
- Calculation:
[tex]\[ V = \pi \times 1.5^2 \times 9 \][/tex]
[tex]\[ V \approx 63.6 \, \text{cubic centimeters} \][/tex]
#### Part H:
- Given: [tex]\( d = 8 \)[/tex] ft, [tex]\( h = 15 \)[/tex] ft
- Calculate radius [tex]\( r = \frac{d}{2} = 4 \)[/tex] ft
- Calculation:
[tex]\[ V = \pi \times 4^2 \times 15 \][/tex]
[tex]\[ V \approx 754.0 \, \text{cubic feet} \][/tex]
#### Part I:
- Given: [tex]\( d = 14 \)[/tex] m, [tex]\( h = 15 \)[/tex] m
- Calculate radius [tex]\( r = \frac{d}{2} = 7 \)[/tex] m
- Calculation:
[tex]\[ V = \pi \times 7^2 \times 15 \][/tex]
[tex]\[ V \approx 2309.1 \, \text{cubic meters} \][/tex]
#### Part J:
- Given: [tex]\( d = 6 \)[/tex] ft, [tex]\( h = 21 \)[/tex] ft
- Calculate radius [tex]\( r = \frac{d}{2} = 3 \)[/tex] ft
- Calculation:
[tex]\[ V = \pi \times 3^2 \times 21 \][/tex]
[tex]\[ V \approx 593.8 \, \text{cubic feet} \][/tex]
### Finding Missing Dimensions
To find a missing height or diameter, rearrange the volume formula to solve for the unknown.
#### Part K:
- Given: [tex]\( d = 3 \)[/tex] in, [tex]\( V = 7.1 \)[/tex] cubic inches
- Calculate radius [tex]\( r = \frac{d}{2} = 1.5 \)[/tex] in
- Finding height [tex]\( h \)[/tex]:
[tex]\[ h = \frac{7.1}{\pi \times 1.5^2} \][/tex]
[tex]\[ h \approx 1 \, \text{inch} \][/tex]
#### Part L:
- Given: [tex]\( d = 11 \)[/tex] ft, [tex]\( V = 190.1 \)[/tex] cubic feet
- Calculate radius [tex]\( r = \frac{d}{2} = 5.5 \)[/tex] ft
- Finding height [tex]\( h \)[/tex]:
[tex]\[ h = \frac{190.1}{\pi \times 5.5^2} \][/tex]
[tex]\[ h \approx 2 \, \text{feet} \][/tex]
#### Part M:
- Given: [tex]\( r = 5 \)[/tex] in, [tex]\( V = 1727.9 \)[/tex] cubic inches
- Finding height [tex]\( h \)[/tex]:
[tex]\[ h = \frac{1727.9}{\pi \times 5^2} \][/tex]
[tex]\[ h \approx 22 \, \text{inches} \][/tex]
#### Part N:
- Given: [tex]\( h = 19 \)[/tex] cm, [tex]\( V = 731.2 \)[/tex] cubic centimeters
- Using radius squared formula
[tex]\[ \pi r^2 = \frac{731.2}{19} \][/tex]
- Finding diameter [tex]\( d \)[/tex]:
[tex]\[ d = 2 \sqrt{\frac{731.2}{\pi \times 19}} \][/tex]
[tex]\[ d \approx 7 \, \text{centimeters} \][/tex]
These steps should help you solve problems involving the calculation of volumes and dimensions of cylinders.
### Volume of Cylinders
The volume [tex]\( V \)[/tex] of a cylinder can be calculated using the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylinder.
#### Part A:
- Given: [tex]\( r = 12 \)[/tex] inches, [tex]\( h = 4 \)[/tex] inches
- Calculation:
[tex]\[ V = \pi \times 12^2 \times 4 \][/tex]
[tex]\[ V \approx 1809.6 \, \text{cubic inches} \][/tex]
#### Part B:
- Given: [tex]\( r = 6 \)[/tex] feet, height uses the result from Part A as [tex]\( h = 1809.6 \)[/tex]
- Calculation:
[tex]\[ V = \pi \times 6^2 \times 1809.6 \][/tex]
[tex]\[ V = 204660.9 \, \text{cubic feet} \][/tex]
#### Part C:
- Given: [tex]\( r = 3 \)[/tex] cm, [tex]\( h = 13 \)[/tex] cm
- Calculation:
[tex]\[ V = \pi \times 3^2 \times 13 \][/tex]
[tex]\[ V \approx 367.6 \, \text{cubic centimeters} \][/tex]
#### Part D:
- Given: [tex]\( r = 9 \)[/tex] m, [tex]\( h = 11 \)[/tex] m
- Calculation:
[tex]\[ V = \pi \times 9^2 \times 11 \][/tex]
[tex]\[ V \approx 2799.2 \, \text{cubic meters} \][/tex]
#### Part E:
- Given: [tex]\( r = 8 \)[/tex] ft, [tex]\( h = 15 \)[/tex] ft
- Calculation:
[tex]\[ V = \pi \times 8^2 \times 15 \][/tex]
[tex]\[ V \approx 3015.9 \, \text{cubic feet} \][/tex]
#### Part F:
- Given: [tex]\( d = 10 \)[/tex] cm, [tex]\( h = 7 \)[/tex] cm
- Calculate radius [tex]\( r = \frac{d}{2} = 5 \)[/tex] cm
- Calculation:
[tex]\[ V = \pi \times 5^2 \times 7 \][/tex]
[tex]\[ V \approx 549.8 \, \text{cubic centimeters} \][/tex]
#### Part G:
- Given: [tex]\( d = 3 \)[/tex] cm, [tex]\( h = 9 \)[/tex] cm
- Calculate radius [tex]\( r = \frac{d}{2} = 1.5 \)[/tex] cm
- Calculation:
[tex]\[ V = \pi \times 1.5^2 \times 9 \][/tex]
[tex]\[ V \approx 63.6 \, \text{cubic centimeters} \][/tex]
#### Part H:
- Given: [tex]\( d = 8 \)[/tex] ft, [tex]\( h = 15 \)[/tex] ft
- Calculate radius [tex]\( r = \frac{d}{2} = 4 \)[/tex] ft
- Calculation:
[tex]\[ V = \pi \times 4^2 \times 15 \][/tex]
[tex]\[ V \approx 754.0 \, \text{cubic feet} \][/tex]
#### Part I:
- Given: [tex]\( d = 14 \)[/tex] m, [tex]\( h = 15 \)[/tex] m
- Calculate radius [tex]\( r = \frac{d}{2} = 7 \)[/tex] m
- Calculation:
[tex]\[ V = \pi \times 7^2 \times 15 \][/tex]
[tex]\[ V \approx 2309.1 \, \text{cubic meters} \][/tex]
#### Part J:
- Given: [tex]\( d = 6 \)[/tex] ft, [tex]\( h = 21 \)[/tex] ft
- Calculate radius [tex]\( r = \frac{d}{2} = 3 \)[/tex] ft
- Calculation:
[tex]\[ V = \pi \times 3^2 \times 21 \][/tex]
[tex]\[ V \approx 593.8 \, \text{cubic feet} \][/tex]
### Finding Missing Dimensions
To find a missing height or diameter, rearrange the volume formula to solve for the unknown.
#### Part K:
- Given: [tex]\( d = 3 \)[/tex] in, [tex]\( V = 7.1 \)[/tex] cubic inches
- Calculate radius [tex]\( r = \frac{d}{2} = 1.5 \)[/tex] in
- Finding height [tex]\( h \)[/tex]:
[tex]\[ h = \frac{7.1}{\pi \times 1.5^2} \][/tex]
[tex]\[ h \approx 1 \, \text{inch} \][/tex]
#### Part L:
- Given: [tex]\( d = 11 \)[/tex] ft, [tex]\( V = 190.1 \)[/tex] cubic feet
- Calculate radius [tex]\( r = \frac{d}{2} = 5.5 \)[/tex] ft
- Finding height [tex]\( h \)[/tex]:
[tex]\[ h = \frac{190.1}{\pi \times 5.5^2} \][/tex]
[tex]\[ h \approx 2 \, \text{feet} \][/tex]
#### Part M:
- Given: [tex]\( r = 5 \)[/tex] in, [tex]\( V = 1727.9 \)[/tex] cubic inches
- Finding height [tex]\( h \)[/tex]:
[tex]\[ h = \frac{1727.9}{\pi \times 5^2} \][/tex]
[tex]\[ h \approx 22 \, \text{inches} \][/tex]
#### Part N:
- Given: [tex]\( h = 19 \)[/tex] cm, [tex]\( V = 731.2 \)[/tex] cubic centimeters
- Using radius squared formula
[tex]\[ \pi r^2 = \frac{731.2}{19} \][/tex]
- Finding diameter [tex]\( d \)[/tex]:
[tex]\[ d = 2 \sqrt{\frac{731.2}{\pi \times 19}} \][/tex]
[tex]\[ d \approx 7 \, \text{centimeters} \][/tex]
These steps should help you solve problems involving the calculation of volumes and dimensions of cylinders.
Thank you for reading the article Did You Hear About Complete each exercise Find the answer in the answer column Write the word under the answer in the box containing the. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
