Question

Circle A has a diameter of 9 inches, a circumference of 28.26 inches, and an area of 63.585 square inches. The diameter of circle B is 5 inches, the circumference is 15.70 inches, and the area is 19.625 square inches..

Part A: Using the formula for circumference, solve for the value of pi for each circle. (4 points)

Part B: Use the formula for area and solve for the value of pi for each circle. (4 points)

Part C: What observation can you make about the value of pi for circles A and B? (2 points)

Answer 1

This is the answer of questions

Answer 2

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

$Area=\pi r^2$

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

$Circumference=2\pi r$   ....(1)

For circle A , $r=\frac{d}{2}= 4.5$ and circumference = 28.26 inches

Putting these values in equation (1) , we get

$28.26=2\pi 4.5\\\\\pi =\frac{28.26}{9} \\\\\pi=3.14$

For circle B , $r=\frac{d}{2}= 2.5$ and circumference = 15.70 inches

Putting these values in equation (1) , we get

$15.70=2\pi 2.5\\\\\pi =\frac{15.70}{5} \\\\\pi =3.14$

Part B :-

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

   $Area=\pi r^2$     ...(2)

For circle A , $r=\frac{d}{2}= 4.5$ and Area = 63.585 square inches

Putting these values in equation (2), we get

$63.585 =\pi(4.5)^2\\\\\pi =\frac{ 63.585 }{20.25} \\\\\pi =3.14$

For circle B , $r=\frac{d}{2}= 2.5$ and Area = 19.625 square inches

Putting these values in equation (2), we get

$19.625=\pi (2.5)^2\\\\\pi =\frac{19.625}{6.25} \\\\\pi =3.14$

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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