To find the area and the circumference of a circle with a diameter of 8 cm, follow these steps:
1. Determine the radius:
- The radius (\(\( r \)\)) is half of the diameter.
- Given the diameter (\(\( d \)\)) is 8 cm.
- Therefore, \(\( r \)\) = \(\( \frac{d}{2} \)\) = \(\( \frac{8 \, \text{cm}}{2} \)\) = 4 cm.
2. Calculate the area (A) of the circle:
- The formula for the area of a circle is \(\( A = \pi r^2 \)\).
- Using \(\( \pi = 3.14 \)\) and \(\( r = 4 \, \text{cm} \)\), we substitute these values into the formula:
\(\( A = 3.14 \times (4 \, \text{cm})^2 \)\)
- Calculate the square of the radius:
\(\( 4 \, \text{cm} \times 4 \, \text{cm} = 16 \, \text{cm}^2 \)\)
- Multiply by \(\( \pi \)\):
\(\( 3.14 \times 16 \, \text{cm}^2 = 50.24 \, \text{cm}^2 \)\)
Therefore, the area of the circle is \(\( 50.24 \, \text{cm}^2 \)\).
3. Calculate the circumference (C) of the circle:
- The formula for the circumference of a circle is \(\( C = \pi d \)\).
- Using \(\( \pi = 3.14 \)\) and \(\( d = 8 \, \text{cm} \)\), we substitute these values into the formula:
\(\( C = 3.14 \times 8 \, \text{cm} \)\)
- Multiply \(\( \pi \)\) by the diameter:
\(\( 3.14 \times 8 \, \text{cm} = 25.12 \, \text{cm} \)\)
Therefore, the circumference of the circle is \(\( 25.12 \, \text{cm} \)\).
In conclusion:
- The area of the circle is \(\( 50.24 \, \text{cm}^2 \)\).
- The circumference of the circle is \(\( 25.12 \, \text{cm} \)\).
