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Problem 205

Geometry Difficulty 1.5 Multiple choice CEMC Gauss (Grade 7) · Canada · 2024

A circle has radius $2$ . If
the radius of the circle is tripled, the area of the original circle
divided by the area of the new circle is

Pick one

Official solution

A circle with radius $2$ has
area $\pi\times2^2=4\pi$ .

If the radius is tripled, then the new radius is $3\times2=6$ .

A circle with radius $6$ has area
$\pi\times6^2=36\pi$ .

The area of the original circle divided by the area of the new circle is
$\frac{4\pi}{36\pi}=\frac{4}{36}=\frac19$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.