The area of a sector of a circle is 88cm
2
and the angle of the sector is 36
∘
. Find the radius (in cm) of the circle. [Use π=
7
22
.]
- A370
- B570
- C70
- D2
70
Solution & Step-by-step Explanation
The formula for the area of a sector of a circle is:
Area of Sector=
360
∘
θ
×πr
2
Given:
Area=88cm
2
θ=36
∘
π=
7
22
Substitute the parameters into the equation:
88=
360
36
×
7
22
×r
2
88=
10
1
×
7
22
×r
2
88=
70
22
×r
2
Isolate r
2
:
r
2
=88×
22
70
r
2
=4×70=280
r=
280
=
4×70
=2
70
cm
Area of Sector=
360
∘
θ
×πr
2
Given:
Area=88cm
2
θ=36
∘
π=
7
22
Substitute the parameters into the equation:
88=
360
36
×
7
22
×r
2
88=
10
1
×
7
22
×r
2
88=
70
22
×r
2
Isolate r
2
:
r
2
=88×
22
70
r
2
=4×70=280
r=
280
=
4×70
=2
70
cm