Question

Two circles are drawn below. The diameter of the smaller circle is a radius of the larger circle. What is the ratio of the smaller circle's circumference to the larger circle's circumference? Give your answer in fully simplified form. It should look like "x:y", where x and y are replaced by integers. [asy] size(4cm); pair o=(0,0); pair x=(0.9,-0.4); draw(Circle(o,sqrt(0.97))); draw(Circle((o+x)/2,sqrt(0.97)/2)); dot(o); dot(x); dot(-x); draw(-x--x); [/asy] Hint(s): Read the question carefully. Does it ask about a ratio of areas? Of radii? Of diameters? Of circumferences? Which question did you answer? Which was asked?

Answer 1

Answer: 1:2

Explanation:

Answer 2

1 : 2

Explanation:

The ratio is ...

small dia : large dia = 1 : 2 = small circumference : large circumference

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Further explanation

The diameter of the small circle is the radius of the large circle. Since the large circle's diameter is twice the length of its radius, the ratio of circle diameters is ...

small : large = 1 : 2

We multiply the diameter by π to get the circumference. Multiplying both these numbers by π will give the ratio of the circumferences. In order to reduce the ratio to lowest terms we must divide by π again:

dia ratio = circumference ratio = lowest terms ratio

1 : 2 = π : 2π = 1 : 2