Final answer:
The area of a circle with a circumference of 10 units can be calculated by first finding the radius using the circumference formula C = 2πr and then using the area formula A = πr². The area is either 25 / π in terms of π or approximately 8.0 square units using π as 3.14 and applying significant figures.
Step-by-step explanation:
To find the area of a circle when the circumference is given, you can use the relationship that the circumference C is equal to 2πr, where r is the radius and π (pi) is approximately 3.14. Since the circumference is given as 10 units, you can solve for the radius r as follows:
C = 2πr
10 = 2πr
r = 10 / (2π)
r = 5 / π
Now that you have the radius, you can calculate the area A using the formula A = πr²:
A = π(5 / π)²
A = π(25 / π²)
A = 25 / π
If you express your answer in terms of π, then A = 25 / π square units. If you use 3.14 for π, then:
A = 25 / 3.14
A ≈ 7.96 square units
To maintain significant figures, since 10 has two significant figures, the area would be approximately:
A = 8.0 square units.