Question

Find the area of the sector of a circle of radius 8 cm and arc with length 15 cm.

Answer 1

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