A gear 15 cm in diameter is turning a gear 21 cm in diameter. When the smaller gear has 105 revolutions, how many has the larger one made?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 75.
The number of revolutions is inversely proportional to the diameter of the gear. So, the ratio of the revolutions is the inverse of the ratio of the diameters.
Smaller gear revolutions / Larger gear revolutions = Larger gear diameter / Smaller gear diameter
Let's denote:
S as the number of revolutions of the smaller gear.
L as the number of revolutions of the larger gear.
Ds as the diameter of the smaller gear.
Dl as the diameter of the larger gear.
We can set up the equation:
S / L = Dl / Ds
We know:
S = 105
Ds = 15 cm
Dl = 21 cm
Plugging in the values:
⇒ 105 / L = 21 / 15
Cross-multiplying:
⇒ 21 × L = 105 × 15
Solving for L:
⇒ L = (105 × 15 ) / 21
Calculating L:
⇒ L = 75
Therefore, the larger gear has made 75 revolutions.