Question

3. If the area of minor sector of a circle with radius
11.2 cm is 49.28 cm, find the measure of the arc.​

Answer 1

Answer:

8.8 cm

Step-by-step explanation:

Here,

Radius of the minor sector, r= 11.2 cm

Area of the minor sector= 49.28cm

To find n, that is the measure of the angle,

Area of minor sector= (n/360)*πr^2

49.28 = (n/360)*(22/7)*11.2*11.2

(4928/100) = (n/360)*(22/7)*(112/10)*(112/10)

(4928/100) = (n/180)*(11/7)*(56/5)*(56/5)

(4928/100) = (n/45)*11*(2/5)*(56*5)

(4928/100)*45*(1/11)*(5/2)*(5/56) = n

(448/20)*45*(1/2)*(5/56) = n

(224/4)*45*(1/56) = n

56*45*(1/56) = n

45°= n

Now,

the length of the arc of the minor sector=

(n/360)*2πr

=(45/360)*2*(22/7)*(11.2)

=(1/8)*2*(22/7)*(112/10)

=(1/4)*22*(16/10)

=22*(4/10)

=88/10

=8.8 cm