Question

The circumference of Circle K is $\pi$ . The circumference of Circle L is $4\pi$ . Two circles, one labeled "Circle K" and the other as "Circle L." What is the value of ratio of their circumferences? Of their radii? Of their areas? Write the ratios as fractions in simplest form.

Answer 1

Explanation:

Given the circumference of Circle K = π

circumference of Circle L = 4π

Ratio of their circumferences = Ck/Cl

Ratio of their circumferences = π/4π

Ratio of their circumferences = 1/4 = 1:4

For their radii

C = 2πr

for circle k with circumference π

π = 2πrk

1 = 2rk

rk = 1/2

for circle l with circumference 4π

4π = 2πr

4 = 2r

r = 4/2

rl = 2

ratio

rk/rl = 1/2/2

rk/rl = 1/4 = 1:4

for the areas

Area of a circle = πr²

for circle k

Ak = π(1/2)²

Ak = π(1/4)

Ak = π/4

for circle l

Al = π(2)²

Al = 4π

Ratio of their areas

Ak/Al = π/4/(4π)

Ak/Al = π/16π

Ak/Al = 1/16 = 1:16