Calculate the circle circumference's upper bound if the area is 400cm(square)
πr^2 = 400
r^2 = 400/π
r = 20/(√π)
circumf = 2πr = 2π(20/√π
= 40√π = appr 70.9
change to whatever you mean by upper bound
Like im not sure is this correct (2pi(n-0.5))
how do you calculate the circumfrance in upper bound
If area is less than 400, then the
radius is less than 20/√π
so, the circumference is less than 40√π
To find the upper bound of the circumference of a circle given its area, we need to determine the largest possible circle that can have an area of 400 square centimeters.
The formula to calculate the area of a circle is: A = πr^2, where A is the area and r is the radius of the circle.
In this case, we have the area (A) as 400 cm². So, we can rearrange the formula to solve for the radius (r): r = √(A/π).
Let's substitute the given area value into the equation: r = √(400/π).
Now, we need to calculate the upper bound of the circumference using the formula: C = 2πr.
Substituting the value of r that we obtained earlier: C = 2π√(400/π).
Simplifying this expression: C = 2√(400π).
Now, we can calculate the approximate value of the upper bound of the circumference.
First, calculate the value of √(400π) using a calculator: √(400π) ≈ 35.58.
Finally, multiply this value by 2: C ≈ 2 * 35.58 ≈ 71.16 cm.
Therefore, the upper bound of the circumference, when the area of the circle is 400 cm², is approximately 71.16 centimeters.