Question

A company manufactures ball bearings for construction equipment. A machine makes the spherical bearings of radius 3 inches, and the process is accurate to 1/100th of an inch. Use differentials to produce an inequality approximating the likely volume of steel in a case containing 100 bearings.

Answer 1

@Michele_Laino

Answer 2

Hint:
total volume \(V\) is:
\[\huge V = 100 \cdot \frac{{4\pi }}{3}{r^3}\]
so, if we compute the first derivative, and we take the finite increments, we get:
\[\huge \Delta V = 100 \cdot 4\pi {r^2} \cdot \Delta r\]
where \(\Delta r= 1/100\)

Answer 3

and \(r=3\)

Answer 4

That makes sense.