find the area of shaded region between the concentric circles of radii 10 cm and 4cm respectively as shown in figure
Answers
Question
In the figure, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC=40
∘
. Consider π=
7
22
Step-by-step explanation:
Answer
Given: Radius of inner circle =7 cm
Radius of outer circle =14 cm
Angle made by sector = 40
o
Area of sector OAC =
360
o
40
o
×πr
2
=
9
1
××
7
22
×14
2
=68.44
Area of sector OBD =
360
o
40
o
×πr
2
=
9
1
××
7
22
×7
2
=17.11
Area of the small region ABDC
= Area of the small sector OAC – Area of the small sector OBD =(68.44−17.11)cm
2
Area of shaded region ABDC= Area of outer circle − Area of inner circle − area of small region ABCD
Area of shaded region ABDC=π×14
2
−π×7
2
−(68.44−17.11)cm
2
Area of shaded region ABDC=410.484 cm
2
Step-by-step explanation:
Given: Radius of inner circle =7 cm
Radius of outer circle =14 cm
Angle made by sector = 40o
Area of sector OAC = 360o40o×πr2
=91××722×142=68.44
Area of sector OBD = 360o40o×πr2
=91××722×72=17.11
Area of the small region ABDC
= Area of the small sector OAC – Area of the small sector OBD =(68.44−17.11)cm2
Area of shaded region ABDC= Area of outer circle − Area of inner circle − area of small region ABCD
Area of shaded region ABDC=π×142−π×72−(68.44−17.11)cm2
Area of shaded region ABDC=410.484 cm2