💡 7th Grade Math (Pre-Algebra): Circles Practice Questions
1
Solved Example
Easy Level
Imagine a perfectly round pizza. If the distance from the center of the pizza to its edge is 7 inches, what is the radius of the pizza?
💡 Key Concept: The radius is the distance from the center of a circle to any point on its edge.
Solution & Explanation
Step 1: Identify what is given. The distance from the center to the edge is given as 7 inches.
Step 2: Recall the definition of the radius. The radius is precisely this distance.
Step 3: State the radius. The radius of the pizza is 7 inches.
👉 The radius is 7 inches.
2
Solved Example
Easy Level
A circular garden has a diameter of 20 feet. What is the radius of the garden?
📌 Tip: The diameter is twice the length of the radius.
Solution & Explanation
Step 1: Understand the relationship between diameter and radius. The formula is \( \text{diameter} = 2 \times \text{radius} \) or \( r = \frac{d}{2} \).
Step 2: We are given the diameter, \( d = 20 \) feet.
Step 3: Calculate the radius using the formula: \( r = \frac{20 \text{ feet}}{2} \).
Step 4: The radius is \( r = 10 \) feet.
✅ The radius of the garden is 10 feet.
3
Solved Example
Easy Level
What is the diameter of a circular clock if its radius is 5 centimeters?
💡 Key Concept: The diameter is the distance across the circle passing through the center.
Solution & Explanation
Step 1: We know that the diameter is twice the radius. The formula is \( d = 2 \times r \).
Step 2: The given radius is \( r = 5 \) centimeters.
Step 3: Substitute the radius into the formula: \( d = 2 \times 5 \text{ cm} \).
Step 4: Calculate the diameter: \( d = 10 \) cm.
👉 The diameter of the clock is 10 centimeters.
4
Solved Example
Medium Level
Calculate the circumference of a circle with a radius of 4 meters. Use \( \pi \approx 3.14 \).
📌 Formula: The circumference \( C \) of a circle is given by \( C = 2 \pi r \), where \( r \) is the radius.
Solution & Explanation
Step 1: Identify the given radius: \( r = 4 \) meters.
Step 2: Use the formula for circumference: \( C = 2 \pi r \).
Step 3: Substitute the values: \( C = 2 \times 3.14 \times 4 \) meters.
Step 4: Perform the multiplication: \( C = 6.28 \times 4 \) meters.
Step 5: Calculate the final circumference: \( C = 25.12 \) meters.
✅ The circumference of the circle is approximately 25.12 meters.
5
Solved Example
Medium Level
Find the circumference of a circle with a diameter of 14 inches. Use \( \pi \approx \frac{22}{7} \).
💡 Key Concept: Circumference can also be calculated using the diameter: \( C = \pi d \).
Solution & Explanation
Step 1: The given diameter is \( d = 14 \) inches.
Step 2: Use the formula for circumference with diameter: \( C = \pi d \).
Step 3: Substitute the values, using \( \pi \approx \frac{22}{7} \): \( C = \frac{22}{7} \times 14 \) inches.
Step 4: Simplify the calculation: \( C = 22 \times \frac{14}{7} \) inches.
Step 5: Calculate the final circumference: \( C = 22 \times 2 \) inches.
Step 6: \( C = 44 \) inches.
👉 The circumference of the circle is 44 inches.
6
Solved Example
Medium Level
Two circular rugs are placed side-by-side. Rug A has a radius of 3 feet, and Rug B has a diameter of 8 feet. Which rug has a larger circumference? Explain your reasoning.
📌 Think: You need to compare their circumferences. Remember the formulas!
- Since \( 8 \pi > 6 \pi \), Rug B has a larger circumference.
✅ Rug B has a larger circumference because \( 8 \pi \) feet is greater than \( 6 \pi \) feet.
7
Solved Example
Real World Example
A bicycle wheel has a diameter of 26 inches. How many inches does the bicycle travel in one full rotation of the wheel? This is equivalent to the circumference of the wheel.
💡 Real-World Connection: Understanding circumference helps us calculate distances traveled by wheels!
Solution & Explanation
Step 1: Identify the given information. The diameter of the bicycle wheel is \( d = 26 \) inches.
Step 2: Recall the formula for circumference using the diameter: \( C = \pi d \).
Step 3: Substitute the diameter into the formula: \( C = \pi \times 26 \) inches.
Step 4: The distance traveled in one rotation is the circumference. We can leave the answer in terms of \( \pi \) or approximate it. Using \( \pi \approx 3.14 \):
- \( C \approx 3.14 \times 26 \) inches.
- \( C \approx 81.64 \) inches.
👉 The bicycle travels approximately 81.64 inches in one full rotation of the wheel.
8
Solved Example
Hard Level
A circular swimming pool has a circumference of 62.8 feet. What is the radius of the pool? Use \( \pi \approx 3.14 \).
📌 Challenge: You need to work backward from the circumference to find the radius.
Solution & Explanation
Step 1: We are given the circumference \( C = 62.8 \) feet and \( \pi \approx 3.14 \).
Step 2: Use the circumference formula: \( C = 2 \pi r \).
Step 3: Substitute the known values into the formula: \( 62.8 = 2 \times 3.14 \times r \).
Step 4: Simplify the right side of the equation: \( 62.8 = 6.28 \times r \).
Step 5: To find the radius \( r \), divide both sides of the equation by 6.28: \( r = \frac{62.8}{6.28} \).
Step 6: Calculate the radius: \( r = 10 \) feet.
✅ The radius of the swimming pool is 10 feet.
7th Grade Math (Pre-Algebra): Circles Practice Questions
Example 1:
Imagine a perfectly round pizza. If the distance from the center of the pizza to its edge is 7 inches, what is the radius of the pizza?
💡 Key Concept: The radius is the distance from the center of a circle to any point on its edge.
Solution:
Step 1: Identify what is given. The distance from the center to the edge is given as 7 inches.
Step 2: Recall the definition of the radius. The radius is precisely this distance.
Step 3: State the radius. The radius of the pizza is 7 inches.
👉 The radius is 7 inches.
Example 2:
A circular garden has a diameter of 20 feet. What is the radius of the garden?
📌 Tip: The diameter is twice the length of the radius.
Solution:
Step 1: Understand the relationship between diameter and radius. The formula is \( \text{diameter} = 2 \times \text{radius} \) or \( r = \frac{d}{2} \).
Step 2: We are given the diameter, \( d = 20 \) feet.
Step 3: Calculate the radius using the formula: \( r = \frac{20 \text{ feet}}{2} \).
Step 4: The radius is \( r = 10 \) feet.
✅ The radius of the garden is 10 feet.
Example 3:
What is the diameter of a circular clock if its radius is 5 centimeters?
💡 Key Concept: The diameter is the distance across the circle passing through the center.
Solution:
Step 1: We know that the diameter is twice the radius. The formula is \( d = 2 \times r \).
Step 2: The given radius is \( r = 5 \) centimeters.
Step 3: Substitute the radius into the formula: \( d = 2 \times 5 \text{ cm} \).
Step 4: Calculate the diameter: \( d = 10 \) cm.
👉 The diameter of the clock is 10 centimeters.
Example 4:
Calculate the circumference of a circle with a radius of 4 meters. Use \( \pi \approx 3.14 \).
📌 Formula: The circumference \( C \) of a circle is given by \( C = 2 \pi r \), where \( r \) is the radius.
Solution:
Step 1: Identify the given radius: \( r = 4 \) meters.
Step 2: Use the formula for circumference: \( C = 2 \pi r \).
Step 3: Substitute the values: \( C = 2 \times 3.14 \times 4 \) meters.
Step 4: Perform the multiplication: \( C = 6.28 \times 4 \) meters.
Step 5: Calculate the final circumference: \( C = 25.12 \) meters.
✅ The circumference of the circle is approximately 25.12 meters.
Example 5:
Find the circumference of a circle with a diameter of 14 inches. Use \( \pi \approx \frac{22}{7} \).
💡 Key Concept: Circumference can also be calculated using the diameter: \( C = \pi d \).
Solution:
Step 1: The given diameter is \( d = 14 \) inches.
Step 2: Use the formula for circumference with diameter: \( C = \pi d \).
Step 3: Substitute the values, using \( \pi \approx \frac{22}{7} \): \( C = \frac{22}{7} \times 14 \) inches.
Step 4: Simplify the calculation: \( C = 22 \times \frac{14}{7} \) inches.
Step 5: Calculate the final circumference: \( C = 22 \times 2 \) inches.
Step 6: \( C = 44 \) inches.
👉 The circumference of the circle is 44 inches.
Example 6:
Two circular rugs are placed side-by-side. Rug A has a radius of 3 feet, and Rug B has a diameter of 8 feet. Which rug has a larger circumference? Explain your reasoning.
📌 Think: You need to compare their circumferences. Remember the formulas!
- Since \( 8 \pi > 6 \pi \), Rug B has a larger circumference.
✅ Rug B has a larger circumference because \( 8 \pi \) feet is greater than \( 6 \pi \) feet.
Example 7:
A bicycle wheel has a diameter of 26 inches. How many inches does the bicycle travel in one full rotation of the wheel? This is equivalent to the circumference of the wheel.
💡 Real-World Connection: Understanding circumference helps us calculate distances traveled by wheels!
Solution:
Step 1: Identify the given information. The diameter of the bicycle wheel is \( d = 26 \) inches.
Step 2: Recall the formula for circumference using the diameter: \( C = \pi d \).
Step 3: Substitute the diameter into the formula: \( C = \pi \times 26 \) inches.
Step 4: The distance traveled in one rotation is the circumference. We can leave the answer in terms of \( \pi \) or approximate it. Using \( \pi \approx 3.14 \):
- \( C \approx 3.14 \times 26 \) inches.
- \( C \approx 81.64 \) inches.
👉 The bicycle travels approximately 81.64 inches in one full rotation of the wheel.
Example 8:
A circular swimming pool has a circumference of 62.8 feet. What is the radius of the pool? Use \( \pi \approx 3.14 \).
📌 Challenge: You need to work backward from the circumference to find the radius.
Solution:
Step 1: We are given the circumference \( C = 62.8 \) feet and \( \pi \approx 3.14 \).
Step 2: Use the circumference formula: \( C = 2 \pi r \).
Step 3: Substitute the known values into the formula: \( 62.8 = 2 \times 3.14 \times r \).
Step 4: Simplify the right side of the equation: \( 62.8 = 6.28 \times r \).
Step 5: To find the radius \( r \), divide both sides of the equation by 6.28: \( r = \frac{62.8}{6.28} \).