Finding the Radius
To determine the radius of the circle, we start with the formula for the circumference (C) of a circle:
- C = 2 * π * r
Given that the circumference is 154 m and π is taken as 22/7, we can rearrange the formula to solve for the radius (r):
- 154 = 2 * (22/7) * r
To isolate r, we perform the following steps:
- First, multiply both sides by 7 to eliminate the fraction:
- 154 * 7 = 2 * 22 * r
- 1078 = 44 * r
- Next, divide both sides by 44:
- r = 1078 / 44
- r = 24.5 m
Thus, the radius of the circle is 24.5 meters.
Calculating the Area
Now that we have the radius, we can find the area (A) of the circle using the formula:
- A = π * r²
Substituting the values into the formula:
- A = (22/7) * (24.5)²
Calculating (24.5)²:
- (24.5)² = 600.25
Now substituting back into the area formula:
- A = (22/7) * 600.25
Calculating the area:
- A = 22 * 600.25 / 7
- A = 13205.5 / 7
- A = 1886.5 m²
Therefore, the area of the circle sheet is approximately 1886.5 square meters.
Summary
- Radius of the circle: 24.5 m
- Area of the circle: 1886.5 m²
This process demonstrates how to relate the circumference of a circle to its radius and area effectively.