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?

Explanation:

Step1: Find radius of smaller circle

Radius of smaller circle \( r_1 = \frac{d_1}{2} = \frac{15}{2} = 7.5 \, \text{mm} \)

Step2: Use radius ratio to find larger radius

Ratio of radii \( r_1:r_2 = 2:3 \), so \( r_2 = \frac{3}{2}r_1 = \frac{3}{2} \times 7.5 = 11.25 \, \text{mm} \)

Step3: Calculate diameter of larger circle

Diameter of larger circle \( d_2 = 2r_2 = 2 \times 11.25 = 22.50 \, \text{mm} \)

Answer:

22.50 mm