the circumference of a circle is 18*3.14cm. The radius is increased, and the circumferenceof the new circle is 16*3.14cm. by how much was the radius of the oringinal circle increased?
C = 2 * r * pi
1 case :
18 * pi = 2 * r * pi Divide both sides by ( 2 * pi )
18 * pi / ( 2 * pi ) = 2 * r * pi / ( 2 * pi )
9 = r
r = 9 cm
2 case :
16 * pi = 2 * r * pi Divide both sides by ( 2 * pi )
16 * pi / ( 2 * pi ) = 2 * r * pi / ( 2 * pi )
8 = r
r = 8 cm
9 - 8 = 1 cm
no
To solve this problem, we can use the formula for the circumference of a circle:
C = 2πr
Let's denote the original radius as "r" and the increased radius as "r + x" (where "x" is the increase in radius).
From the given information, we have:
C₁ = 18π cm
C₂ = 16π cm
Using the formula for circumference, we can write two equations as follows:
For the original circle:
C₁ = 2πr
For the new circle with an increased radius:
C₂ = 2π(r + x)
Substituting the given values, we have:
18π = 2πr (equation 1)
16π = 2π(r + x) (equation 2)
Dividing both equations by 2π, we can simplify to:
9 = r (equation 3)
8 = r + x (equation 4)
Subtracting equation 3 from equation 4, we can find the value of x (the increase in radius):
8 - 9 = x
Therefore, the radius of the original circle was increased by (-1) cm.
To solve this problem, we need to compare the circumferences of the original and new circles and find the difference. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Given that the original circle's circumference is 18*3.14 cm, we can set up the equation as follows:
18*3.14 = 2πr (equation 1)
Similarly, for the new circle with a circumference of 16*3.14 cm:
16*3.14 = 2π(r + x) (equation 2)
(where x represents the increase in the radius).
We can simplify equation 2 by dividing both sides by 2π:
16*3.14 / 2π = r + x
Simplifying further, we have:
8*3.14 / π = r + x
To find the increase in the radius (x), we need to subtract the original radius (r) from the sum of the original radius and the increase in radius (r + x):
x = (r + x) - r
Simplifying, we get:
x = r
Therefore, the increase in the radius is equal to the original radius.