Question

A sector 75 is removed from a circle of radius 10•5m. What area of the circle is left use ^ = 22/7

Answer 1

Appropriate Question:-

• A sector of 75° is removed from a circle of radius 10.5m. What area of the circle left? Use π = 22/7.

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Given:-

• Centre Angle of Sector = 75°

• Radius of Circle = 10.5 m

To Find:-

• Area of the Remaining Circle.

Formula Used:-

• ${\boxed{\bf{Area\: of\: Sector= \dfrac{θ}{360°}\times \pi r^2}}}$

• ${\boxed{\bf{Area\: of\: Circle=\pi r^2}}}$

Solution:-

Firstly,

$\bf :\implies\:Area\: of\: Sector= \dfrac{θ}{360°}\times \pi r^2$

Here,

• θ = 75°

• r = 10.5 m

Putting values,

$\tt :\implies\:Area\: of\: Sector= \dfrac{75°}{360°}\times \pi \times 10.5^2$

$\tt :\implies\:Area\: of\: Sector= \dfrac{5}{24}\times \pi \times 110.25$

$\tt :\implies\:Area\: of\: Sector= \dfrac{551.25}{24}\times \pi$

$\tt :\implies\:Area\: of\: Sector= 22.96\pi \: m^2$

And,

$\tt :\implies\:Area\: of\: Circle= \pi r^2$

$\tt :\implies\:Area\: of\: Circle= \pi \times 10.5^2$

$\tt :\implies\:Area\: of\: Circle= 110.25\pi \:m^2$

Now,

$\bf :\implies\:Area\: of\: Remaining\: Circle=Area\: of\: Circle - Area\: of\: Sector$

$\tt :\implies\:Area\: of\: Remaining\: Circle=110.25\pi - 22.96\pi$

$\tt :\implies\:Area\: of\: Remaining\: Circle=87.29\pi$

$\tt :\implies\:Area\: of\: Remaining\: Circle=87.29 \times \dfrac{22}{7}$

$\tt :\implies\:Area\: of\: Remaining\: Circle=\dfrac{1920.28}{7}$

$\tt :\implies\:Area\: of\: Remaining\: Circle=274.34\:m^2$

Hence, The Area of Remaining of Circle is 274.34 m².

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