A certain hydraulic system is designed to exert a force 100 times as large as the one put into it. (a) What must be the ratio of the area of the slave cylinder to the area of the master cylinder

Ratio is 100:1

Explanation:

From hydraulic press formulas;

(F1/A1) = (F2/A2)

Applying this to the question, we can say that Force on slave cylinder (Fs) = F1 while Force on master cylinder (Fm) = F2 and their respective Areas as As and Am.

Now plugging it into the equation to obtain;

Fs/As = Fm/Am

Now, the question says the hydraulic system is designed to exert a force 100 times as big as the one put into it, thus;

Fs = 100 Fm

And so from the equation earlier, rearranging, we have,

Fs/Fm = As/Am. So, 100Fm/Fm = As/Am

So, Fm will cancel out and we have ;

As/Am = 100/1

Thus, the ratio of the area of the slave cylinder to the master cylinder is 100:1