AREAS RELATED
TO CIRCLE
Sol.
O
28 cm
A
X
B
Radius of quadrant (r) = 28 cm
ar (AXB) =
ar (O – AXB)
–
ar (Δ OAB)
What is the formula to find area of sector?
?
θ
360
πr2
✔
Central angle (θ) =
360
6
= 60º
✔
ar(O-AXB)
=
θ
360
× πr2
=
60
360
×
22
7
× 28
× 28
1
6
1
4
2
3
=
22 × 2 × 28
3
=
1232
3
410.67 cm2
=
ar (O-AXB)
∴
410.67 cm2
=
✔
i.e. we need to find area of six segments
Cost = Rate × Area
✔
?
Let us first find area of 1 segment
Sol.
–
Radius of quadrant (r) = 28 cm
Central angle (θ) =
360
= 60º
ar (ΔOAB)
=
4
× (side)2
=
4
×
(28)2
=
4
×
28 × 28
1
7
=
×
7 × 28
=
1.7
×
7 × 28
=
333.2 cm2
∴
ar (ΔOAB)
ar (AXB) =
ar (O – AXB)
–
✔
✔
O
28 cm
A
X
B
ar (Δ OAB)
6
What is the formula to find area of an equilateral triangle?
4
×
(Side)2
ΔOAB is an equilateral triangle
Sol.
ar (AXB) =
ar (O – AXB)
–
✔
✔
O
28 cm
A
X
B
ar (AXB) =
ar (O – AXB)
–
ar (Δ OAB)
=
410.67
–
333.2
=
77.47 cm2
ar (Δ OAB)
∴
Area of 6 segment
=
6
× 77.47
=
464.82 cm2
Area of 1 segment
=
77.47
Cost = Rate × Area
∴
Area of 6 segment
Cost
= Rate × Area
=
0.35 ×
464.82
=
162.68
Total cost of making designs is162.68
∴
ar (AXB)
ar (O-AXB) = 410.67 cm2
ar (ΔOAB) = 333.2 cm2