AREAS RELATED
TO CIRCLE
Sol.
BROOCH
Q. A brooch is made with silver wire in the form of a circle with
diameter 35 mm. The wire is also used in making 5 diameters
which divide the circle into 10 equal sectors as shown in figure.
Find : (i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.
Radius (r)
=
35
2
mm
Total length of the wire
=
Circumference
+
5 (Diameters)
Diameter = 2r
=
2πr
+
5 (2r)
=
2r
[ π + 5 ]
=
2 ×
35
2
22
7
+
5
=
2 ×
35
2
22 + 35
7
=
2 ×
35
2
×
57
7
5
=
5 × 57
Total length of the wire is 285 mm
∴
What is the formula to find circumference of circle?
2πr
×
×
× πr2
Area of each sector =
θ
360
5
11
Radius (r)
=
35
2
mm
Central angle =
36º
360
10
=
=
36
360
×
22
7
×
35
2
×
35
2
10
2
=
11 × 35
4
Area of each sector is 96.25 mm2
∴
=
385
4
= 96.25 mm2
What is the formula to find area of sector?
?
✔
θ
360
πr2
Sol.
Q. A brooch is made with silver wire in the form of a circle with
diameter 35 mm. The wire is also used in making 5 diameters
which divide the circle into 10 equal sectors as shown in figure.
Find : (i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.