Q. What is π ?
Q. Show that the area of a circle is πr^2 . ( Where 'r' is radius of circle )
Q. Show that the circumference of a circle is 2π r . ( Where 'r' is radius of circle )
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the π =pie the value substituted to this symbol is 22 upon 7 the area of circle is πr Square becoz The usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pitimes the radius. ... This give a geometric justification that the area of a circle really is "pi r squared"π is defined to be the ratio of the circumference of a circle over its diameter (or 2 times its radius).
This ratio is a constant since all circles are geometrically similar and linear proportions between any similar geometric figures are constant.
If you were looking for how the value of the ratio π is calculated or how we know that the same ratio applies to the area of a circle
hope it helps you mark as BRAINLIEST ✌✌✌
the π =pie the value substituted to this symbol is 22 upon 7 the area of circle is πr Square becoz The usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pitimes the radius. ... This give a geometric justification that the area of a circle really is "pi r squared"π is defined to be the ratio of the circumference of a circle over its diameter (or 2 times its radius).
This ratio is a constant since all circles are geometrically similar and linear proportions between any similar geometric figures are constant.
If you were looking for how the value of the ratio π is calculated or how we know that the same ratio applies to the area of a circle
hope it helps you mark as BRAINLIEST ✌✌✌
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Answers :-
Q. What is pi ?
A. Pi (π) is a mathematical constant that is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes written as pi.
Q. Show area of circle is pi r^2 ?
A. The area of triangle AOB is 1/2 ( base × height) = 1/2 (s × r)
However, we can make 8 such triangles inside the octagon as show below:
This means that the area of the entire octagon is 8 ×( 1/2 (s × r)) = 1/2 r × 8s
Notice that 8s is equal to the perimeter of the octagon
As stated before, if we increase the number of sides to infinity or a very big number, the resulting n-gon ( The regular polygon which number of sides is a big number) will will almost look like a circle
This means that the perimeter of the octagon will almost be the same as the perimeter of the circle
As a result, the closer the perimeter of the polygon is to the circle, the closer the area of the polygon is to the area of the circle
It is reasonable then to replace 8s by 2 × pi × r, which is the perimeter of the circle, to calculate the area of the polygon or the circle when the number of sides is very big
Doing so we get:
Area of circle or polygon equal = 1/2 r × 2 × pi × r = pi × r2
Answers :-
Q. What is pi ?
A. Pi (π) is a mathematical constant that is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes written as pi.
Q. Show area of circle is pi r^2 ?
A. The area of triangle AOB is 1/2 ( base × height) = 1/2 (s × r)
However, we can make 8 such triangles inside the octagon as show below:
This means that the area of the entire octagon is 8 ×( 1/2 (s × r)) = 1/2 r × 8s
Notice that 8s is equal to the perimeter of the octagon
As stated before, if we increase the number of sides to infinity or a very big number, the resulting n-gon ( The regular polygon which number of sides is a big number) will will almost look like a circle
This means that the perimeter of the octagon will almost be the same as the perimeter of the circle
As a result, the closer the perimeter of the polygon is to the circle, the closer the area of the polygon is to the area of the circle
It is reasonable then to replace 8s by 2 × pi × r, which is the perimeter of the circle, to calculate the area of the polygon or the circle when the number of sides is very big
Doing so we get:
Area of circle or polygon equal = 1/2 r × 2 × pi × r = pi × r2
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