how many sectors of 90 degree will fit inside of a circle with a radius of 5 cm?

Answer 1

Jon S.'s comment above is valid - a sector is the area within a central angle of a circle. Since there are 360 degrees in a circle, there are 360/90 = 4 ninety degree consecutive central angles in a circle. The area of the circle is π·r². A 90 degree sector, then, has 1/4th of the area of a full circle, or (π·r²)/4. Your circle has a radius of 5 cm, so a 90 degree sector has an area of (π·5²)/4 = 25π/4 cm².