Verified answer

This is the same as saying that the larger gear has 10 gear teeth and the smaller gear has 4 gear teeth.

The 4 teeth on the small gear will mesh with the larger gear. So, for every 4 teeth on the large gear the smaller will rotate once.

so, if the larger gear rotates once the smaller will rotate 10/4 = 2.5 times

or, if the large gear rotates 10 times the smaller will rotate 25 times....e.t.c.

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If the radius of gear A is 10, its circumference is 2 * pi * r, or 2 * pi * 10, or 20 pi. If the radius of gear B is 4, its circumference is 2 * pi * r, or 2 * pi * 4, or 8 pi. So the ratio is 20 pi / 8 pi , or 2.5. Note that you really don't have to deal with the "pi" because they will always cancel out; I just did that to show that the ratio of the radii is the same as the ratio of the circumference. So you can simply take the radius of the larger gear divided by the radius of the smaller gear, and that will show you how many times the smaller gear will rotate for each rotation of the larger gear.

Answer: 10/4, or 2.5.

Circumference of Gear A: 2πr = 2π(10) = 20π

Circumference of Gear B: 2πr = 2π(4) = 8π

The smaller gear will naturally complete more revolutions than the larger gear.

Gear B will rotate: 20π/8π = 2.5 times