Let's solve each problem step-by-step for calculating the volume of cylinders.
1. **Find the volume of a cylinder with a height of 12 inches and a diameter of 8 inches.**
- Formula: \( V = \pi r^2 h \)
- Given: Diameter \( d = 8 \) inches, so the radius \( r = \frac{d}{2} = 4 \) inches, and height \( h = 12 \) inches.
- Calculation: \( V = 3.14 \times 4^2 \times 12 = 3.14 \times 16 \times 12 = 3.14 \times 192 = 602.88 \) cubic inches.
So, the correct answer is **602.88 cubic inches**.
2. **Find the volume of a cylinder with a height of 6 cm, a radius of 3 cm.**
- Formula: \( V = \pi r^2 h \)
- Given: Radius \( r = 3 \) cm, height \( h = 6 \) cm.
- Calculation: \( V = 3.14 \times 3^2 \times 6 = 3.14 \times 9 \times 6 = 3.14 \times 54 = 169.56 \) cubic centimeters.
So, the correct answer is **169.56 cubic centimeters**.
3. **Find the volume of a peanut butter jar with a height of 16 cm and a diameter of 10 cm.**
- Formula: \( V = \pi r^2 h \)
- Given: Diameter \( d = 10 \) cm, so the radius \( r = \frac{d}{2} = 5 \) cm, and height \( h = 16 \) cm.
- Calculation: \( V = 3.14 \times 5^2 \times 16 = 3.14 \times 25 \times 16 = 3.14 \times 400 = 1256 \) cubic centimeters.
So, the correct answer is **1,256 cubic centimeters**.
4. **Find the volume of a salsa jar with a height of 6 inches and a radius of 2 inches.**
- Formula: \( V = \pi r^2 h \)
- Given: Radius \( r = 2 \) inches, height \( h = 6 \) inches.
- Calculation: \( V = 3.14 \times 2^2 \times 6 = 3.14 \times 4 \times 6 = 3.14 \times 24 = 75.36 \) cubic inches.
So, the correct answer is **75.36 cubic inches**.
5. **Find the volume of a water tower with a height of 25 meters and a diameter of 16 meters.**
- Formula: \( V = \pi r^2 h \)
- Given: Diameter \( d = 16 \) meters, so the radius \( r = \frac{d}{2} = 8 \) meters, and height \( h = 25 \) meters.
- Calculation: \( V = 3.14 \times 8^2 \times 25 = 3.14 \times 64 \times 25 = 3.14 \times 1600 = 5024 \) cubic meters.
So, the correct answer is **5,024 cubic meters**.
Summary of correct answers:
1. 602.88 cubic inches
2. 169.56 cubic centimeters
3. 1,256 cubic centimeters
4. 75.36 cubic inches
5. 5,024 cubic meters
Volume of Cylinders Quick Check
1. Find the volume of a cylinder with a height of 12 inches and a diameter of 8 inches. Use 3.14 for pi.(1 point)
Responses
1,808.64 cubic inches
1,808.64 cubic inches
150.72 cubic inches
150.72 cubic inches
602.88 cubic inches
602.88 cubic inches
2,411.52 cubic inches
2. Use the image to answer the question.
A 3 D oblique cylinder shows a length of 8 centimeters and perpendicular height of 6 centimeters. The base radius is 3 centimeters.
Find the volume of the cylinder.- Use 3.14 for pi.
(1 point)
Responses
226.08 cubic centimeters
226.08 cubic centimeters
339.12 cubic centimeters
339.12 cubic centimeters
169.56 cubic centimeters
169.56 cubic centimeters
678.24 cubic centimeters
678.24 cubic centimeters
3. A jar of peanut butter has a height of 16 centimeters and a width of 10 centimeters. Find the volume of the peanut butter jar. Use 3.14 for pi.(1 point)
Responses
2,009.6 cubic centimeters
2,009.6 cubic centimeters
1,256 cubic centimeters
1,256 cubic centimeters
4,019.2 cubic centimeters
4,019.2 cubic centimeters
5,024 cubic centimeters
4. A jar of salsa has a height of 6 inches and a radius of 2 inches. Find the volume of the salsa jar. Use 3.14 for pi.(1 point)
Responses
56.52 cubic inches
56.52 cubic inches
75.36 cubic inches
75.36 cubic inches
226.08 cubic inches
226.08 cubic inches
18.84 cubic inches
5. A water tower has a height of 25 meters and a width of 16 meters. What is the volume of the water tower? Use 3.14 for pi.(1 point)
Responses
7,850 cubic meters
7,850 cubic meters
20,096 cubic meters
20,096 cubic meters
5,024 cubic meters
5,024 cubic meters
15,700 cubic meters
3 answers
u sure?
Yes, let's double-check each calculation to ensure the answers are correct.
1. **Volume of a cylinder with height 12 inches and diameter 8 inches:**
- Diameter \( d = 8 \) inches gives radius \( r = \frac{8}{2} = 4 \) inches.
- Height \( h = 12 \) inches.
- Volume \( V = \pi r^2 h = 3.14 \times 4^2 \times 12 = 3.14 \times 16 \times 12 \).
- \( 3.14 \times 16 = 50.24 \).
- \( 50.24 \times 12 = 602.88 \).
The correct volume is **602.88 cubic inches**.
2. **Volume of a cylinder with height 6 cm and radius 3 cm:**
- Radius \( r = 3 \) cm.
- Height \( h = 6 \) cm.
- Volume \( V = \pi r^2 h = 3.14 \times 3^2 \times 6 = 3.14 \times 9 \times 6 \).
- \( 3.14 \times 9 = 28.26 \).
- \( 28.26 \times 6 = 169.56 \).
The correct volume is **169.56 cubic centimeters**.
3. **Volume of a peanut butter jar with height 16 cm and diameter 10 cm:**
- Diameter \( d = 10 \) cm gives radius \( r = \frac{10}{2} = 5 \) cm.
- Height \( h = 16 \) cm.
- Volume \( V = \pi r^2 h = 3.14 \times 5^2 \times 16 = 3.14 \times 25 \times 16 \).
- \( 3.14 \times 25 = 78.5 \).
- \( 78.5 \times 16 = 1256 \).
The correct volume is **1,256 cubic centimeters**.
4. **Volume of a salsa jar with height 6 inches and radius 2 inches:**
- Radius \( r = 2 \) inches.
- Height \( h = 6 \) inches.
- Volume \( V = \pi r^2 h = 3.14 \times 2^2 \times 6 = 3.14 \times 4 \times 6 \).
- \( 3.14 \times 4 = 12.56 \).
- \( 12.56 \times 6 = 75.36 \).
The correct volume is **75.36 cubic inches**.
5. **Volume of a water tower with height 25 meters and diameter 16 meters:**
- Diameter \( d = 16 \) meters gives radius \( r = \frac{16}{2} = 8 \) meters.
- Height \( h = 25 \) meters.
- Volume \( V = \pi r^2 h = 3.14 \times 8^2 \times 25 = 3.14 \times 64 \times 25 \).
- \( 3.14 \times 64 = 200.96 \).
- \( 200.96 \times 25 = 5024 \).
The correct volume is **5,024 cubic meters**.
All the answers have been confirmed to be accurate.
1. **Volume of a cylinder with height 12 inches and diameter 8 inches:**
- Diameter \( d = 8 \) inches gives radius \( r = \frac{8}{2} = 4 \) inches.
- Height \( h = 12 \) inches.
- Volume \( V = \pi r^2 h = 3.14 \times 4^2 \times 12 = 3.14 \times 16 \times 12 \).
- \( 3.14 \times 16 = 50.24 \).
- \( 50.24 \times 12 = 602.88 \).
The correct volume is **602.88 cubic inches**.
2. **Volume of a cylinder with height 6 cm and radius 3 cm:**
- Radius \( r = 3 \) cm.
- Height \( h = 6 \) cm.
- Volume \( V = \pi r^2 h = 3.14 \times 3^2 \times 6 = 3.14 \times 9 \times 6 \).
- \( 3.14 \times 9 = 28.26 \).
- \( 28.26 \times 6 = 169.56 \).
The correct volume is **169.56 cubic centimeters**.
3. **Volume of a peanut butter jar with height 16 cm and diameter 10 cm:**
- Diameter \( d = 10 \) cm gives radius \( r = \frac{10}{2} = 5 \) cm.
- Height \( h = 16 \) cm.
- Volume \( V = \pi r^2 h = 3.14 \times 5^2 \times 16 = 3.14 \times 25 \times 16 \).
- \( 3.14 \times 25 = 78.5 \).
- \( 78.5 \times 16 = 1256 \).
The correct volume is **1,256 cubic centimeters**.
4. **Volume of a salsa jar with height 6 inches and radius 2 inches:**
- Radius \( r = 2 \) inches.
- Height \( h = 6 \) inches.
- Volume \( V = \pi r^2 h = 3.14 \times 2^2 \times 6 = 3.14 \times 4 \times 6 \).
- \( 3.14 \times 4 = 12.56 \).
- \( 12.56 \times 6 = 75.36 \).
The correct volume is **75.36 cubic inches**.
5. **Volume of a water tower with height 25 meters and diameter 16 meters:**
- Diameter \( d = 16 \) meters gives radius \( r = \frac{16}{2} = 8 \) meters.
- Height \( h = 25 \) meters.
- Volume \( V = \pi r^2 h = 3.14 \times 8^2 \times 25 = 3.14 \times 64 \times 25 \).
- \( 3.14 \times 64 = 200.96 \).
- \( 200.96 \times 25 = 5024 \).
The correct volume is **5,024 cubic meters**.
All the answers have been confirmed to be accurate.
4 answers