A gauge is used to measure the diameter of a ball. Determine the radius of the balls if their diameters are 30mm and 20mm, and the vertical distances from the top of the gauge to their centers are 4.2

Step 1: Identify the given dimensions.
The diameter of the larger ball is $D_1 = 30$ mm, so its radius is $R_1 = \frac{30}{2} = 15$ mm.
The diameter of the smaller ball is $D_2 = 20$ mm, so its radius is $R_2 = \frac{20}{2} = 10$ mm.
The vertical distance from the top of the gauge to the center of the larger ball is $H_1 = 4.25$ mm.
The vertical distance from the top of the gauge to the center of the smaller ball is $H_2 = 36.75$ mm.

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