Question

What is the circumference, in centimeters, of a circle with an area of 49π cm^2?

a) 14π cm
b) 28π cm
c) 49π cm
d) 98π cm

Answer 1

(a) 14π cm

Step-by-step explanation:

the circumference (C) of a circle (C) is calculated as

C = 2πr ( r is the radius )

to find r, use the given area

the area (A) of a circle is calculated as

A = πr²

given A = 49π cm² , then

πr² = 49π ( divide both sides by π )

r² = 49 ( take square root of both sides )

`√(r^2)` =
`√(49)` , that is

r = 7

Then

C = 2π × 7 = 14π cm

Answer 2

The circumference of the circle is 14π cm.

Step-by-step explanation:

To find the circumference of a circle, we can use the formula C=2πr, where C is the circumference and r is the radius of the circle. Given that the area of the circle is 49π cm², we can find the radius using the formula A=πr², where A is the area and r is the radius. Rearranging the formula, we get r=√(A/π). Substituting the given values, we have r=√(49π/π)=√49=7 cm. Finally, substituting the value of the radius into the formula for the circumference, we get C=2π(7)=14π cm.