The larger circle has a radius that is 18 inches longer than the smaller circle. The larger circle has a circumference that is A pi feet larger then the smaller circle. find the value of a.
Radius of smaller circle: a-18 (inchs)
Radius of larger circle: a (inchs)
Circumference of smaller circle:
2*pi*(a-18)=2*pi*a-2*pi*18=2*pi*a-36*pi (inchs)
Circumference of larger circle:
2*pi*a (inchs)
Difference betwen ircumference of smaller and large circle:
D=2*pi*a-(2*pi*a-36pi)=
2*pi*a-2*pi*a+36pi=
36*pi (inchs)
D=36*pi (inchs)
1feet=12 inchs
D=(36*pi)=(3*pi)ft
D=(A*pi)
A*pi=3*pi Divide with pi
A=3
D=(36*pi)in=(3*pi)ft
To find the value of A, we need to use the formulas for the circumference of a circle.
Let's denote the radius of the smaller circle as r.
According to the information given, the radius of the larger circle is 18 inches longer than the radius of the smaller circle, which means the radius of the larger circle is r + 18.
The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius.
For the smaller circle:
C1 = 2πr
For the larger circle:
C2 = 2π(r + 18)
The problem states that the circumference of the larger circle is A pi feet larger than the circumference of the smaller circle. In other words, we have the equation:
C2 - C1 = Aπ
Substituting the formulas for C1 and C2, we get:
2π(r + 18) - 2πr = Aπ
Simplifying the equation, we have:
2πr + 36π - 2πr = Aπ
The 2πr terms cancel out, leaving us with:
36π = Aπ
To find the value of A, we divide both sides of the equation by π:
36 = A
Therefore, the value of A is 36.