You have 100 feet of fencing with which to construct a circular pen. what is the area can you enclose?
To find the area that can be enclosed with 100 feet of fencing while constructing a circular pen, we need to use the formula for the circumference of a circle and then calculate the radius and area.
1. Start by using the formula for the circumference of a circle: C = 2πr, where C represents the circumference and r represents the radius of the circle.
2. Rearrange the formula to solve for r: r = C / (2π).
3. Substitute the given value of the circumference (fencing) into the formula: C = 100 feet.
r = 100 feet / (2π) = 100 / (2 × 3.14) ≈ 15.92 feet (rounding to two decimal places).
4. Once you have calculated the radius, you can find the area of the circular pen using the formula for the area of a circle: A = πr^2, where A represents the area.
5. Substitute the value of the radius found in step 3 into the formula:
A = 3.14 × (15.92 feet)^2 ≈ 795.77 square feet (rounding to two decimal places).
Therefore, you can enclose approximately 795.77 square feet of area with 100 feet of fencing when constructing a circular pen.