Final answer:
The area of the circle is 36π square yards and the circumference is 12π yards. When rounded to the nearest whole number, the area is approximately 113 square yards and the circumference is approximately 38 yards.
Step-by-step explanation:
To find the area and circumference of a circle with a radius of 6 yards, we use two key formulas derived from geometry. The ancient Greeks discovered these methods over 2000 years ago and they remain fundamental in mathematics today.
Area of a Circle
The area (A) of a circle is given by the formula A = πr². With a radius (r) of 6 yards, the area is:
A = π × 6² = π × 36 = 36π square yards
Circumference of a Circle
The circumference (C) of a circle is given by the formula C = 2πr. Thus, with our radius of 6 yards, the circumference is:
C = 2 π × 6 = 12π yards
Expressed in terms of π, the area is 36π square yards and the circumference is 12π yards. To give approximate values, we round these results to the nearest whole number using the approximation π ≈ 3.14:
Area = 36 × 3.14 ≈ 113 square yards (rounded)
Circumference = 12 × 3.14 ≈ 38 yards (rounded)