5. Sam has a circular chicken pen. The fence surrounding the pen is 48 feet long. How many square feet does the chicken pen cover? Round your answer to the nearest square foot.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
In this case, the circumference is 48 feet. So, 48 = 2πr.
Simplifying the equation, we divide both sides by 2π: r = 48 / 2π = 7.64 feet.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
Plugging in the value of r, the area is A = π(7.64)^2 = 183.21 square feet.
Therefore, the chicken pen covers approximately 183 square feet.
To find the area of the circular chicken pen, you'll need to use the formula for the area of a circle.
The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius.
However, we don't have the radius of the pen, but we do have the circumference of the pen, which is given as 48 feet.
The formula for the circumference of a circle is C = 2πr.
Let's solve for r using the circumference formula:
C = 2πr
48 = 2πr
Divide both sides of the equation by 2π to solve for r:
r = 48 / (2π)
We can use 3.14 as an approximation for π.
r ≈ 48 / (2 * 3.14) ≈ 7.64 feet
Now that we have the radius, we can calculate the area of the circular chicken pen using the area formula:
A = πr^2
A = 3.14 * 7.64^2
A ≈ 183.04 square feet
Therefore, the chicken pen covers approximately 183 square feet.
To find the area of the circular chicken pen, we need to know the radius of the circle.
Since the fence surrounding the pen is 48 feet long, we can use this information to calculate the circumference of the circle.
The formula to find the circumference of a circle is given by:
C = 2πr,
where C is the circumference and r is the radius.
We can rearrange the formula to solve for the radius:
r = C / (2π).
We can substitute the given circumference (48 feet) into the formula:
r = 48 / (2π).
Now that we have the radius, we can calculate the area of the circle using the formula:
A = πr^2,
where A is the area and r is the radius.
Substituting the value of the radius into the formula:
A = π * (48 / (2π))^2.
Simplifying the equation, we get:
A = π * (24 / π)^2.
A = π * 24^2 / π^2.
A = 576π / π^2.
A ≈ 183.43 square feet.
Rounding the answer to the nearest square foot, the chicken pen covers approximately 183 square feet.