I need help on the following please?
A group of clowns performs in a ring with an area of about 2,123 square feet. What is the circumference of the ring? Choose the closest answer.
156 ft.
52 ft.
163 ft.
82 ft.
Thank You. Please explain the answer
Hi Christopher,
Let me explain the method of solving this problem:
Given the area of the ring = 2123 ft^2
The formula for area is pi*r^2, where r is the radius
Therefore,we need to find the r based on the area given
2123 ft^2 = pi*r^2 (work this out using calculator)
r^2 = (2123ft^2)/pi
r = 26 ft
We now know what is r.The formula of circumference of a circle is pi*D,where D is the diameter & we all know that diameter = 2*radius
So, D = 2*26ft = 52 ft
Hence, circumference = pi*D
= pi*52ft
= 163.36 ft
The closest answer is 163 ft.Thats all!
Hope my explanation has made you understand clearly. Good luck :)
Omg I hate clowns haha.
So the area of a circle is A=pi(r^2), and you know that the area of the circle is 2,123 square feet, right? So just set them equal as 2,123=pi(r^2), and solve for r, or the radius.
Just divide both sides by pi and then square root both sides. Now that you have your radius, plug it in to the circumference formula, C=pi(d), d being the diamater.
You would multiply the radius by two, since the radius is half the diameter, and then multiply that by pi.
Hope it works! If you can, try to use the pi button, not just 3.14, since it makes it more accurate.
To find the circumference of a circle, you can use the formula C = 2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
In this case, we are given the area of the ring, which is 2,123 square feet.
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius.
Since we are given the area, we can rearrange the formula to solve for the radius. Dividing both sides of the equation by π, we get r^2 = A/π, and taking the square root of both sides, we find r = √(A/π).
Now, we can substitute the given area into the equation to find the radius: r = √(2,123/π).
Using a calculator or rounding π to 3.14159 for simplicity, we have r ≈ √(2,123/3.14159) ≈ √676.08 ≈ 26.01 feet (rounded to two decimal places).
Finally, we can use the circumference formula to find the circumference: C = 2πr ≈ (2)(3.14159)(26.01) ≈ 163.05 feet.
Among the provided choices, the closest answer to the circumference of the ring is 163 ft.