What is the ratio of the circumferences for two circles with areas 6π m2 and 150π m2?
Mathematics · High School · Tue Nov 03 2020
Answered on
Given:
Area of Circle 1: 6π m^2
Area of Circle 2: 150π m^2
Determine the Circumference.
Circumference of the Circle Formula:
C = 2πr
Area of the Cirlce Formula:
A = πr^2
r = √A/π
Solution:
Since we are given the area, we must first find the radius of the circles before finding the circumference.
Radius of Circle 1:
r = √6π m^2/π
r = √6m^2
r = 2.45m
Radius of Circle 2:
r = √150π m^2/π
r = √150m^2
r = 12.25m
Now we can easily solve the circumference of the two circles by substituting the values of r to the formula for the circumference of the cirlce.
Circumference of Circle 1:
C = 2π(2.45m)
C = 4.9π m
Circumference of Circle 2:
C = 2π(12.25m)
C = 24.50π m
The given answers can be expressed in ratio as,
4.9π m:24.50π m
Final answer:
Circumference of Circle 1:Circumference of Circle 2
4.9π m:24.50π m