A circle has a 3cm radius.
1. By what factor does the circumference change if the radius is tripled? Explain.
2. By what factor does the area change if the radius is doubled? Explain.
C=2pI*radius
if rad goes up by 3, C goes up by 3
area=pi*(rad)^2
double rad, area goes up by 22
1. To find out how the circumference changes when the radius is tripled, we need to first understand the formula for the circumference of a circle. The formula is C = 2πr, where C represents the circumference and r represents the radius.
Given that the original radius is 3 cm, we can calculate the original circumference as C1 = 2π(3) = 6π cm.
When the radius is tripled, the new radius becomes 3 * 3 = 9 cm. We can calculate the new circumference as C2 = 2π(9) = 18π cm.
Now, to find the factor by which the circumference changes, we divide the new circumference by the original circumference: C2 / C1 = (18π) / (6π) = 3.
Therefore, the circumference changes by a factor of 3 when the radius is tripled. This means the new circumference is three times larger than the original circumference.
2. To determine how the area changes when the radius is doubled, we need to know the formula for the area of a circle. The formula is A = πr^2, where A represents the area and r represents the radius.
Given that the original radius is 3 cm, we can calculate the original area as A1 = π(3)^2 = 9π cm^2.
When the radius is doubled, the new radius becomes 2 * 3 = 6 cm. We can calculate the new area as A2 = π(6)^2 = 36π cm^2.
To find the factor by which the area changes, we divide the new area by the original area: A2 / A1 = (36π) / (9π) = 4.
Therefore, the area changes by a factor of 4 when the radius is doubled. This means the new area is four times larger than the original area.