Asked by Anonymous
An arc of a circle is of length 5p cm and the sector is bounds has an area of
20p cm^2
find the radius of the circle.
20p cm^2
find the radius of the circle.
Answers
Answered by
Reiny
let the radius be r
circumference = 2πr
area = πr^2
πr^2/20π = 2πr/5π
r^2/20 = 2r/5
5r^2 = 40r
r^2 - 8r = 0
r(r-8) = 0
r = 8 or r = 0, of course we would want r > 0 to any area at all
r = 8
check:
if r = 8
circumf= 16π
area= 64π
20π/64π = 5/16
5π/16π = 5/16
All looks good
circumference = 2πr
area = πr^2
πr^2/20π = 2πr/5π
r^2/20 = 2r/5
5r^2 = 40r
r^2 - 8r = 0
r(r-8) = 0
r = 8 or r = 0, of course we would want r > 0 to any area at all
r = 8
check:
if r = 8
circumf= 16π
area= 64π
20π/64π = 5/16
5π/16π = 5/16
All looks good
Answered by
Anonymous
thank u @reiny