Question

For the diagram, calculate; the radius of the smaller section and the perimeter of the shape of the and;

Answer 1

a). Radius r of the small sector= 12cm

b). Perimeter of the shape= 68 cm

c). Angle= 47.7°

Explanation:

a). Radius of the big sector= 24 cm

Arc if the big sector= 20 cm

Arc of the small sector= 10 cm

For the radius r of the small sector

r/10 = 24/20

r=(10*24)/20

r= 24/2

r= 12 cm

Radius r of the small sector= 12cm

b). Perimeter of the shape

= Total length of the shape

Let's note that the other side of the sector is also the radius= 24 cm

Perimeter= 20+24+24

Perimeter of the shape= 68 cm

c) the angle

Length of arc = 2πr*(angle/360)

Let angle = b

Length of arc = 20cm

20= 2*3.14*24*(b/360)

(20*360)/(2*3.14*24)= b

47.7°= b

Angle= 47.7°