Math question paper on area and circumference of circle

Here’s a simple math question paper focusing on the area and circumference of a circle. These problems range from basic to intermediate level.

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### **Math Question Paper: Area and Circumference of a Circle**

#### **Part A: Basic Problems**

1. **Find the Circumference:**
   A circle has a radius of 7 cm. Calculate its circumference.
   
   *Formula: Circumference = $ 2\pi r $*

2. **Find the Area:**
   A circle has a diameter of 14 cm. Calculate its area.
   
   *Formula: Area = $ \pi r^2 $*

3. **Radius from Circumference:**
   The circumference of a circle is 31.4 cm. Find the radius of the circle. (Use $ \pi = 3.14 $)

4. **Find the Diameter:**
   A circle has an area of 50.24 cm². What is the diameter of the circle? (Use $ \pi = 3.14 $)

5. **Circumference from Area:**
   A circle has an area of 154 cm². Find the circumference of the circle. (Use $ \pi = 3.14 $)

#### **Part B: Word Problems**

6. **Walking Around a Circular Park:**
   A park is in the shape of a circle with a radius of 21 meters. If a person walks along the boundary of the park, how far will they walk in one complete round?

7. **Area of a Circular Garden:**
   The diameter of a circular garden is 20 meters. Calculate the area of the garden.

8. **Comparison of Two Circles:**
   The radius of Circle A is twice that of Circle B. If the area of Circle B is 78.5 cm², what is the area of Circle A?

9. **Cost of Fencing:**
   A circular field has a radius of 35 meters. If fencing costs $5 per meter, what will be the total cost to fence the entire boundary of the field?

10. **Shaded Area in a Circle:**
    A circular tablecloth has a radius of 15 cm. A smaller circle with a radius of 5 cm is cut out from the center. Find the area of the remaining cloth.

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### **Formulas Reminder:**
- **Circumference of a Circle** = $ 2\pi r $
- **Area of a Circle** = $ \pi r^2 $
- **Radius** = $ \frac{\text{Circumference}}{2\pi} $
- **Diameter** = $ 2r $

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Would you like to discuss any particular questions or see the solutions?

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### **Relative Questions:**

1. How does the circumference of a circle change when the radius is doubled?
2. If you know the diameter, how would you calculate the radius?
3. How would you find the area if only the circumference is given?
4. What is the relationship between the area of two circles with different radii?
5. How can you solve for the radius if the area of the circle is known?

**Tip:** Always keep in mind the difference between the radius and diameter; the radius is half the diameter!

Explore a variety of math problems focusing on the area and circumference of a circle. This set of questions is ideal for students in Grades 6-8, covering essential concepts in geometry, including calculating area, circumference, radius, and diameter with detailed formulas.

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