Calculate the area of a circle

Example 1: Using the radius

Find the area of a circle with radius 14 cm. Use π = 22/7.

Solution

$Area = \pi r^2$ $Area = \frac{22}{7} \times 14 \times 14$ $Area = \frac{22 \times 196}{7}$ $Area = 22 \times 28$ $Area = 616 \text{ cm}^2$

Therefore, the area of the circle is 616 cm².

Example 2: Using the diameter

Find the area of a circle with diameter 21 dm. Use π = 22/7.

Solution

First, find the radius: $r = \frac{d}{2} = \frac{21}{2} = 10.5$ dm

$Area = \pi r^2$ $Area = \frac{22}{7} \times 10.5 \times 10.5$ $Area = \frac{22}{7} \times 110.25$ $Area = 346.5 \text{ dm}^2$

Therefore, the area of the circle is 346.5 dm².

Example 3: From circumference to area

The circumference of a circle is 88 m. Find its area. Use π = 22/7.

Solution

Step 1: Find the diameter from the circumference.

$C = \pi d$ $88 = \frac{22d}{7}$ $d = 88 \times \frac{7}{22} = 28 \text{ m}$

Step 2: Find the radius.

$r = \frac{d}{2} = \frac{28}{2} = 14 \text{ m}$

Step 3: Calculate the area.

$Area = \pi r^2$ $Area = \frac{22}{7} \times 14 \times 14$ $Area = 616 \text{ m}^2$

Therefore, the area of the circle is 616 m².

1. Identify whether you have been given the radius or the diameter.
2. If given the diameter, divide by 2 to get the radius.
3. Use the formula A = πr² (or A = πd²/4).
4. Substitute the values and multiply.
5. Write the answer with the correct unit squared (cm², m², dm², mm²).

• Area of a circle = πr² (using radius)
• Area of a circle = πd²/4 (using diameter)
• Remember: radius = diameter ÷ 2
• Use π = 22/7 or 3.14 as directed in the question

In Tanzania, farmers and fishpond owners often need to know the area of circular fish ponds to calculate how many fish to stock or how much water treatment is needed. For example, if a circular fish pond has a diameter of 28 metres, the area would be 616 square metres. If a farmer hires a labourer to clean the pond at a rate of 2,000 Tanzanian shillings per square metre, they would pay 616 × 2,000 = 1,232,000 shillings for the job. Knowing how to calculate the area helps with planning and budgeting for such work.