two circles have circumference of 10p cm and 12p cm. what is the difference in their radii
2 pi R2 = 12
2 pi R1 = 10
R2 - R1 = 12/(2 pi) - 10/(2 pi)
= 2/(2 pi)
= 1/pi
To find the difference in radii between two circles, we need to determine the radii of the circles first.
The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius.
Let's solve for the radius of the first circle:
C₁ = 10π cm
10π = 2πr₁ (equating C₁ to the formula for circumference)
Divide both sides of the equation by 2π:
r₁ = 10π / 2π
r₁ = 5 cm
Now, let's solve for the radius of the second circle:
C₂ = 12π cm
12π = 2πr₂ (equating C₂ to the formula for circumference)
Divide both sides of the equation by 2π:
r₂ = 12π / 2π
r₂ = 6 cm
Finally, we can calculate the difference in radii:
Difference in radii = r₂ - r₁
Difference in radii = 6 cm - 5 cm
Difference in radii = 1 cm
Therefore, the difference in radii between the two circles is 1 cm.