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Question
Find the area of the sector of a circle of radius 8 cm and arc with length 15 cm.
Solution
Radius of circle = OA = r = 8 cm
Length of arc = l = 15 cm
Length of arc = `"angle made by arc at centre"/360 xx 2pi xx "radius"`
∴ I = `(∠"AOB")/360 xx 2pir`
∴ 15 = `(∠"AOB")/360 xx 2 xx pi xx 8`
∴ 15 × 360 = ∠AOB × 16 × π
∴ 15 × 90 = ∠AOB × 4 × π
∴ 1350 = ∠AOB × 4 × π
∴ 337.5 = ∠AOB × π
∴ ∠AOB = 337.5/ π
Area of sector = `"angle of sector"/360 xx pi xx "radius"^2`
`"Area of sector AOB = "(∠"AOB")/360 xx pir^2`
`"Area of sector" = (337.5/pi)/360 xx pi xx 8^2`
`"Area of sector" = 337.5/(360 xx pi) xx pi xx 8^2 = (337.5 xx 64)/360`
`"Area of sector" = (337.5 xx 8)/45 = 2700/45`
∴ area of sector = 60 cm2
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