Question

the ratio of the radii of two circles is 2:3. the diameter of the smaller circle is 15 mm. what is the length of the diameter of the larger circle?

10.00 mm
11.25 mm
22.50 mm
30.00 mm

Explanation:

Relate the ratio of radii to the ratio of diameters

$$ \frac{r_1}{r_2} = \frac{2}{3} \implies \frac{d_1}{d_2} = \frac{2r_1}{2r_2} = \frac{2}{3} $$

Set up the proportion with the given smaller diameter

$$ \frac{15}{d_2} = \frac{2}{3} $$

Solve for the larger diameter

$$ d_2 = 15 \times \frac{3}{2} = 22.50\text{ mm} $$

Answer:

• 10.00 mm
• 11.25 mm
• 22.50 mm (Correct answer)
• 30.00 mm