Question

(7)
OAB is a sector of the circle having
centre at O and radius 12 cm. If
mZAOB = 45°, find the difference
between the area of sector OAB and
sector AOB.​

Answer 1

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vaibhavaim1995

Secondary SchoolMath 5+3 pts

OAB is the sector of circle having centre at O and radius = 12cm. If measure of angle AOB = 45°,find the difference between area of sector OAB and sector AOB

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vaibhavaim1995

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Answer:

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}

Area of the circle A=\pi r^{2}

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

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

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}

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

= \pi r^{2} (\frac{7}{8} )

Difference between area of sector AOB and OAB

=\frac{7}{8} \pi r^{2} -\frac{1}{8} \pi r^{2}

=\frac{6}{8} \pi r^{2}

=\frac{3}{4} \pi r^{2}

=\frac{3}{4} \times\frac{22}{7} \times12\times12

= 339.43 cm²