Circles: word problems

key notes :

Key Formulas to Remember

Radius and Diameter:

d=2r,r=d/2

Circumference (Perimeter of Circle):

C=2πr or C=πd

Area of Circle:

A=πr2

👉 Use π=3.14 or 22/7.

Steps to Solve Word Problems

1. Read the problem carefully.
2. Identify whether you need radius, diameter, area, or circumference.
3. Write the formula clearly.
4. Substitute the given values into the formula.
5. Solve step by step and write the final answer with correct units.

Solved Word Problems

Example 1: Finding circumference

A circular garden has a radius of 7 m. Find its circumference.

C=2πr=2×22/7×7=44 m

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Example 2: Finding area

A circular park has diameter 14 m. Find its area.

• Radius = 14/2=7 m

A=πr²=22/7×7×7=154 m²

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Example 3: From circumference to diameter

The circumference of a wheel is 62.8 cm. Find its radius.

C=2πr  ⟹  r=C/2π=62.8/(2×3.14)=10 cm

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Example 4: Real-life application

A wire is bent in the form of a circle with radius 14 cm. Find the length of the wire.

Length of wire=Circumference=2πr=2×22/7×14=88 cm

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Example 5: Find area from diameter

A circular table has a diameter of 2 m. Find its area.

• Radius = 1 m

A=πr²=3.14×1²=3.14 m²

Practice Questions

1. Find the circumference of a circle with diameter 28 cm.
2. A circular pond has a radius of 21 m. Find its area.
3. The circumference of a circular track is 440 m. Find its radius (use π=22/7​).
4. A circular park has a diameter of 20 m. Find its area and circumference.
5. A rope is tied around a circular field of radius 35 m. Find the length of the rope and the area of the field.

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📌 Important Tip:

• Perimeter (Circumference) → linear units (cm, m)
• Area → square units (cm², m²)

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Learn with an example

Let’s practice!🖊️