Question

A circle has a sector with area \dfrac{45}{4}\pi 4 45 ​ πstart fraction, 45, divided by, 4, end fraction, pi and central angle of \purple{\dfrac{9}{10}\pi} 10 9 ​ πstart color #9d38bd, start fraction, 9, divided by, 10, end fraction, pi, end color #9d38bd radians . What is the area of the circle?

Answer 1

Answer:

Therefore,

$Area\ of\ Circle = 25\pi \ units^{2}$

Step-by-step explanation:

Given:

$Area\ of\ sector = \dfrac{45}{4}\pi$

$Central\ angle =\theta = \dfrac{9}{10}\pi$ ( in Radians)

To Find:

Area of Circle = ?

Solution:

If "θ" is measured in radians then area of sector is given by,

$Area\ of\ sector = \dfrac{1}{2}\times r^{2}\theta$

Where,

θ = Central angle in radians

r =radius of a circle

Substituting the values we get

$\dfrac{45}{4}\pi= \dfrac{1}{2}\times r^{2}\times \dfrac{9}{10}\pi$

On solving we get

$r^{2}=25\\\\Square\ Rooting\\\\r = \sqrt{25}=5\ units$

Now, Area of Circle is given by,

$Area\ of\ Circle = \pi r^{2}$

Substituting the values we get

$Area\ of\ Circle = 25\pi \ units^{2}$

Therefore,

$Area\ of\ Circle = 25\pi \ units^{2}$

Answer 2

Answer:

10 pi cm square

Step-by-step explanation:

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