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