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Byju's Answer
Standard VII
Mathematics
Major Arc, Minor Arc and Semicircular Arc
i The perimet...
Question
(i) The perimeter of a sector of a circle is 58 cm. Find the area if its diameter is 9 cm.
(ii) Find the area of a sector whose radius and perimeter are 20 cm and 110 cm respectively.
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Solution
i)
D
=
4
㎝
⇒
r
=
9
2
=
4.5
㎝
θ
360
°
×
2
π
r
+
2
r
=
58
㎝
⇒
θ
360
°
×
2
×
22
7
×
4.5
+
2
×
4.5
=
58
198
θ
360
°
×
7
+
9
=
58
⇒
θ
=
7
×
360
°
198
(
58
−
9
)
=
623.64
°
Area
=
θ
360
°
×
π
r
2
=
623.64
°
360
°
×
22
7
×
4.5
×
4.5
=
110.25
㎠
ii)
θ
360
°
×
2
π
r
+
2
r
=
110
㎝
⇒
θ
360
°
×
2
×
22
7
×
20
+
(
2
×
20
)
=
110
㎝
⇒
880
θ
360
°
×
7
=
70
㎝
⇒
θ
=
70
×
360
°
×
7
880
=
200.45
°
Area
=
θ
360
°
×
π
r
2
=
200.45
°
360
°
×
22
7
×
20
×
20
=
699.98
㎠
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