Question

4) The area of a piece of pie in the shape of a sector is 7.1 in. The angle of the sector is 40°. Find the diameter of
the circle.

Answer 1

Answer:

Step-by-step explanation:

Area of sector = angle/360 * pi * r^2

7.1 = 40/360 * 22/7 * r^2

7.1 = 1/9 * 22/7 * r^2

63.9 = 22r^2/7

r^2 = (7 * 63.9)/22

r^2 = 20.331818181818

r = square root of 20.331818181818

r = 4.51

d = r * 2 = 4.51 * 2 = 9.02

Answer 2

The diameter of circle is $9.02 inch$

Area of sector :

The area of sector is given as,

                      $Area=\frac{\theta}{360} *\pi r^{2}$

Where r is radius of circle and $\theta$ is angle of sector.

Given that, area is 7.1 and $\theta=40$

Substitute values in above relation.

              $7.1=\frac{40}{360}*3.14*r^{2} \\\\r^{2}=\frac{7.1*360}{40*3.14}=20.35\\ \\ r=\sqrt{20.35}=4.5$

The diameter of circle is,$=2r=2*4.51=9.02inch$

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