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Jovanny · Answer 1 · 2024-11-26T09:50:04+0000

Concept

Circumference - The circumference of a circle is the length of the circle's boundary. If you cut a circle and straighten it, the length of the edge will be the length of the circumference. The formula for calculating perimeter is Circumference = 2πr

Where r is the radius of the circle

Area - The area of a circle is the area occupied by the circle in the two-dimensional plane. This is easily determined using the formula

where r is the radius of the circle.

Given

We have been given that circle A of diameter 9 inches having circumference of 28.26 inches and an area of 63.585 square inches. Circle B of diameter 5 inches having circumference of 15.70 inches, and the area of 19.625 square inches.

Find

We are asked to determine the value of pi by using circumference and area formula .

Solution

Part A :-

We will use the formula of the circumference of the circle which is given by

$Circumference=2\pi r$

For circle A ,
r=(d)/(2)=4.5 and circumference = 28.26 inches

Putting these values in equation (1) ,

we get

$28.26=2\pi 4.5$

$\pi =(28.26)/(9)\\ \pi =3.14$

For circle B ,
r=(d)/(2) = 2.5 and circumference = 15.70 inches

Putting these values in equation (1) , we get

$15.70=2\pi 2.5\\\pi =(15.70)/(5\\) \\\pi = 3.14$

Part B :-

We will use the formula of the area of the circle which is given by

$Area=\pi r^(2)$

For circle A ,
r=(d)/(2) = 4.5 and Area = 63.585 square inches

Putting these values in equation (2), we get

$19.625=\pi (2.5)^(2) \\\pi =(19.625)/(6.25) \\\pi =3.14$

Part C :-

The value of pi for both of the circle is same which is 3.14 by using circumference as well as area formula .

Therefore , the value of pi is constant which is equals to 3.14 .

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