Question

7) OAB is a sector of the circle havin
centre at 0 and radius 12 cm. 1
mZAOB = 45°, find the differenc
between the area of sector OAB an
sector AOB​

Answer 1

339.43 cm²

Step-by-step explanation:

Given the radius of the circle r = 12 cm

Angle subtended by the arc AB at the centre θ = 45°

Area of sector with radius r and angle in degrees θ, is given by

\frac{\theta}{360^\circ} \times\pi r^{2}360∘θ×πr2

Area of the circle  A=\pi r^{2}A=πr2

Area of the sector OAB = \frac{45^\circ}{360^\circ} \times\pi r^{2}360∘45∘×πr2

                                       = \frac{1}{8} \times\pi r^{2}81×πr2

Area of sector AOB can be calculated as Area of the Circle -  Area of sector OAB

∴ Area of sector AOB

= \pi r^{2} -\frac{1}{8} \pi r^{2}=πr2−81πr2

= \pi r^{2} (1-\frac{1}{8} )=πr2(1−81)

= \pi r^{2} (\frac{7}{8} )=πr2(87)

Difference between area of sector AOB and OAB

=\frac{7}{8} \pi r^{2} -\frac{1}{8} \pi r^{2}=87πr2−81πr2

=\frac{6}{8} \pi r^{2}=86πr2

=\frac{3}{4} \pi r^{2}=43πr2

=\frac{3}{4} \times\frac{22}{7} \times12\times12=43×722×12×12

= 339.43 cm