Question
Download Solution PDFThe area of a sector of a circle having radius 14 cm is 231 cm2. Find the degree measure of the corresponding central angle. (Use π = 22/7)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius of the circle, r = 14 cm
Area of the sector, A = 231 cm2
π = 22/7
Formula Used:
Area of a sector = (θ / 360) × π × r2
where θ is the central angle in degrees.
Calculation:
⇒ (θ / 360) × (22/7) × 142 = 231
⇒ (θ / 360) × (22/7) × 196 = 231
⇒ (θ / 360) × 616 = 231
⇒ θ / 360 = 231 / 616
⇒ θ / 360 = 0.375
⇒ θ = 0.375 × 360
⇒ θ = 135
The degree measure of the corresponding central angle is 135º.
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