Question

The diagram shows a sector of a circle, centre 0, radius 5r.
The length of the arc AB is 4r.
Find the area of the sector in terms of r, giving your answer in its simplest form.

Answer 1

Answer:

10r²

Step-by-step explanation:

given

radius (R) = 5r

length of the arc is 4r

length of the arc with radius (R) = x/360° *2πR

so

according to data

x/360 *2πR = 4r

multiply with R on both sides

x/360 * 2πR² = 4r*R

area of sector = 4r *(5r)/2

20r²/2

10r²