Question

What is the circumference of a circle with an area of 36π? Possible Answers: None of the other answers 12π 6π 15π 32 Correct answer: 12π Explanation: We know that the area of a circle can be expressed: a = πr2 If we know that the area is 36π, we can substitute this into said equation and get: 36π = πr2 Solving for r, we get: 36 = r2; (after taking the square root of both sides:) 6 = r Now, we know that the circuference of a circle is expressed: c = πd.  Since we know that d = 2r (two radii, placed one after the other, make a diameter), we can rewrite the circumference equation to be: c = 2πr Since we have r, we can rewrite this to be: c = 2π*6 = 12π​

Answer 1

Answer:

The area of a circle with radius

r

is given by

A

=

π

⋅

r

2

and the circumference

by

S

=

2

⋅

π

⋅

r

But

A

=

36

⋅

π

⇒

π

⋅

r

2

=

36

⋅

π

⇒

r

=

6

c

m

hence

S

=

2

⋅

π

⋅

6

=

12

⋅

π

cm