Question

Find the area of a sector

Answer 1

990 cm²

Explanation:

Given ratio of radii = a : b , then

ratio of areas = a² : b²

Here

ratio of radii = 50 : 30 = 5 : 3 , then

ratio of areas = 5² : 3² = 25 : 9

let x be the area of sector DEF , then using proportion

`(25)/(2750)` =
`(9)/(x)` ←
`(ratio)/(area)`

cross- multiply

25x = 24750 ( divide both sides by 25 )

x = 990

Area of sector DEF = 990 cm²