Question

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

Answer 1

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