Question

1. here are four circles, their radius or diameter lengths, and their areas.

write a formula to calculate the exact area of a circle, a, with a radius, r. use these examples and your work from problems 2 - 3 if it is helpful.

Explanation:

Step1: Recall the formula for the area of a circle

The area \(A\) of a circle is given by the formula \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Verify with the given examples

• For the first circle with \(r = 2m\), \(A=\pi\times(2)^{2}=4\pi\approx 12.57m^{2}\) (since \(\pi\approx3.14\), \(4\times3.14 = 12.56\approx12.57\)).
• For the second circle with \(r = 4in\), \(A=\pi\times(4)^{2}=16\pi\approx50.27in^{2}\) (since \(16\times3.14 = 50.24\approx50.27\)).
• For the third circle with \(r = 35cm\), \(A=\pi\times(35)^{2}= 1225\pi\approx3846.5cm^{2}\approx3848.45cm^{2}\) (if we take \(\pi\approx3.1416\), \(1225\times3.1416=3848.46\)).
• For the fourth circle, the diameter \(d = 50cm\), so \(r=\frac{d}{2}=25cm\). Then \(A=\pi\times(25)^{2}=625\pi\approx 1962.5cm^{2}\approx1963.50cm^{2}\) (if \(\pi\approx3.1416\), \(625\times3.1416 = 1963.5\)).

Answer:

\(A=\pi r^{2}\)