Question

If Ꮎ =π\4
and 1 = 44 cm, then find the value of 'r'.
4​

Answer 1

Answer:

The formula for finding the area A of a circle is: A = πr², where r is the radius of the circle, and, for this problem, let's let the famous irrational number π= 3.14.

The formula for finding the circumference C of a circle is: C = 2πr. Solving for radius r in terms the circumference C, we get:

C = 2πr

C/(2π) = (2πr)/(2π)

C/(2π) = [(2π)/(2π)]r

C/(2π) = [1]r

r = C/(2π), but C = 44 cm; therefore, we have:

r = (44 cm)/(2π)

Now, substituting this result into the formula for the area of a circle, we get:

A = πr²

= π[(44 cm)/(2π)]²

= π(44 cm)²/(2π)² by the Power of a Quotient Property for positive integral exponents

= π[(44 cm)(44 cm)]/[(2π)(2π)]

= π[1936 cm²]/[4π²]

= π[1936 cm²]/[(4)(π²)]

= π[1936 cm²/4](1/π²)

= [1936 cm²/4](π/π²)

= 484 cm²(1/π)

= 484 cm²/π

= 484 cm²/3.14

= 154.14 cm² is the area of the given circle (rounded to 2 decimal places).