Answer:
990 cm²
Step-by-step 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
[tex]\frac{25}{2750}[/tex] = [tex]\frac{9}{x}[/tex] ← [tex]\frac{ratio}{area}[/tex]
cross- multiply
25x = 24750 ( divide both sides by 25 )
x = 990
Area of sector DEF = 990 cm²
