Question
Download Solution PDFThe area of a sector of a circle is 88 sq. cm, and the angle of the sector is 45º. Find the radius of the circle. (Use \(\pi = \frac{22}{7}\))
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The area of a sector of a circle is 88 sq. cm, and the angle of the sector is 45º.
Concept used:
1. Area of a sector = (πR2) × \(\frac {θ}{360}\) (R = Radius of the circle and θ = Angle of of the sector)\
2. π = \(\frac {22}{7}\)
Calculation:
Let the radius of the circle be R cm.
According to the question,
(π × R2) × \(\frac {45}{360}\) = 88
⇒ (\(\frac {22}{7}\) × R2) × \(\frac {1}{8}\) = 88
⇒ R2 = (4 × 7 × 8)
⇒ R = 4√14
∴ The radius of the circle is 4√14 cm.
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