Question

The diagram shows a quadrant with a perimeter of 30cm. Find its radius . Give answers in terms of pi

Answer 1

r =
`(60)/(\pi +4)`

Explanation:

the arc length is calculated as

arc = circumference of circle × fraction of circle

= 2πr ×
`(90)/(360)` ( r is the radius )

= 2πr ×
`(1)/(4)`

=
`(1)/(2)` πr

the perimeter (P) is the sum of the length of arc + 2 radii and P = 30 , so

`(1)/(2)` πr + 2r = 30 ( multiply through by 2 to clear the fraction )

πr + 4r = 60 ← factor out r from each term on the left side )

r(π + 4) = 60 ← divide both sides by (π + 4)

r =
`(60)/(\pi +4)`