Chapter 11.7, Problem 43HP

To determine

Find the number of revolutions the smaller gear makes in that time.

Answer to Problem 43HP

The smaller gear makes 96 number of revolution.

Explanation of Solution

Given:

A gear that is 8 inches in diameter turns a smaller gear that is 3 inches in diameter. If the larger gear makes 36 revolutions, how many revolutions does the smaller gear make in that time?

Concept Used:

A gear covers distance in 1 revolution is its circumference.

Calculation:

A gear covers distance in 1 revolution is its circumference.

Distance covers the big gear in 1 revolution with 8 inches diameter = $\text{π}·\text{d}=8\text{π}$

Distance covers the big gear in 36 revolutions = $8\text{π}·36=288\text{π}$

Distance covers the small gear in 1 revolution with 3 inches diameter = $\text{π}·\text{d}=3\text{π}$

Let the number of revolution the smaller gear makes = x

Distance covers the small gear in x revolutions = $3\text{π}·x$

The required equation:

Distance covers the big gear in 36 revolutions = Distance covers the small gear in x revolutions

  $3\text{π}·x=288\text{π}\Rightarrow \text{x}\text{=}\frac{288\text{π}}{3\text{π}}=96$

The smaller gear makes 96 number of revolution.

Thus, the smaller gear makes 96 number of revolution.