Question

The Relationship between Circumference & Area Practice

Answer 1

1. A circle has a circumference of 10 units. Calculate the area of the circle.

Solution:
Circumference = 2πr = 10 units
r = 10 / 2π = 5 / π ≈ 1.59 units
Area = πr^2 ≈ π(1.59)^2 ≈ π(2.53) ≈ 7.94 square units

2. A circle has an area of 25 square units. Calculate the circumference of the circle.

Solution:
Area = πr^2 = 25 square units
r^2 = 25 / π
r ≈ √(25 / π) ≈ √7.96 ≈ 2.82 units
Circumference = 2πr ≈ 2π(2.82) ≈ 17.72 units

3. A circle has a circumference of 18 units. Calculate the area of the circle.

Solution:
Circumference = 2πr = 18 units
r = 18 / 2π = 9 / π ≈ 2.86 units
Area = πr^2 ≈ π(2.86)^2 ≈ π(8.16) ≈ 25.65 square units

4. A circle has an area of 36 square units. Calculate the circumference of the circle.

Solution:
Area = πr^2 = 36 square units
r^2 = 36 / π
r ≈ √(36 / π) ≈ √11.46 ≈ 3.38 units
Circumference = 2πr ≈ 2π(3.38) ≈ 21.24 units

5. A circle has a circumference of 14 units. Calculate the area of the circle.

Solution:
Circumference = 2πr = 14 units
r = 14 / 2π = 7 / π ≈ 2.23 units
Area = πr^2 ≈ π(2.23)^2 ≈ π(4.97) ≈ 15.64 square units