If a circle has twice the diameter, is it twice as large or 4 times as large

richiesmasher

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Hi let's say we have a circle of diameter 15cm, and another circle of diameter 30cm.

Is the second circle 4 times as large, or twice as large.

Using the circumference formula I'll find out that the circumference doubles, but using the area formula I'll see that the area quadruples, so what is the correct thing to say? is the second cirlce twice or four times as large?

Area of circle 1=pi*r2
A1= pi*(d/2)2 = pi*d2/4

Area of circle 2 = pi*2(d2/4) = pi*4d2/4= pi*d2

So the ratio of the areas of the two circles is (d^2)/((d^2)/4)

So that will work out to 4:1
But using the circumference I'll get 2:1
 
If the Linear Measure ratio is 2:1,
The Area Measure ratio will be 2^2:1^1 ==> 4:1, and
The Volume Measure ratio will be 2^3:1^3 ==> 8:1

Count the number of dimensions being compared.
 
If a circle has twice the diameter, is it twice as large or 4 times as large …

Using the circumference formula I'll find out that the circumference doubles, but using the area formula I'll see that the area quadruples, so what is the correct thing to say? is the second cirlce twice or four times as large?
The circumference is twice as large, and the area is four times as large.

Doubling the diameter doubles the circumference, holding four times as much area as before.
 
Hi let's say we have a circle of diameter 15cm, and another circle of diameter 30cm.

Is the second circle 4 times as large, or twice as large.

Using the circumference formula I'll find out that the circumference doubles, but using the area formula I'll see that the area quadruples, so what is the correct thing to say? is the second cirlce twice or four times as large?

The statement "the circle is ___ times as large" is just ambiguous. Without stating whether you mean circumference, area, or something else, we can't be sure what you are saying.

Note that for some people, a "circle" is a curve, and circumference is what they think of as its size; for others a "circle" is a disk (the interior of the circle); and for yet others, it might he the dimensions (radius or diameter) that they have in mind. What "size" means depends on your purpose and your perspective.

So you have to ask what someone else means, and make your intent clear when you yourself speak.
 
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