let the radius of circle R be r
let the radius of circle W be w
recall that arclength = rØ, where Ø is the angle in radians
arc length on first circle = (π/2)r
arc length of 2nd circle = (π/3)w
but they are equal
πr/2 = πw/3
r = 3w/2
area of first sector = (1/4)πr^2
= (1/4)π(9w^2)/4
= (9/16)πw^2
area of 2nd sector = (1/6)π w^2
ratio of first area : second area
= (9/16)π w^2 : (1/6)π w^2
= 9/16 : 1/6
= 54 : 16
= 27 : 8
or 27/8 as a fraction
check my arithmetic
If a central angle of 90 degrees defines an arc on circle R that has the same length as the arc on circle W defined by a 60-degree central angle, what is the ratio of the area of circle R to the area of circle W? Express your answer as a common fraction.
5 answers
since the arc lengths are the same,
90r = 60w
So, r/w = 2/3
Since the areas vary as the square of the radii,
R/W = = (r/w)^2 = 4/9
90r = 60w
So, r/w = 2/3
Since the areas vary as the square of the radii,
R/W = = (r/w)^2 = 4/9
Steve is right,
I can't be bothered to find my error in all my mess.
I can't be bothered to find my error in all my mess.
360 / 60 = 6
Yes