The number of uniform spherical balls that can be produced from a given mass of lead is inversely proportional to the radius of the ball cubed. If 2744 balls can be made when the radius is 1mm, how many balls can be made when the radius is 1.4mm ?

So first we need to write down the proportionality relationship the question states. If we let n be the number of balls and r be the radius of the balls we can say n (proportional symbol) 1/r³. We can turn this into an equation by replacing the proportion symbol with an "=" and multiplying the rhs by a constant which we will call k. So we have n = k/r³. Putting in the numbers given in this question we can solve for k :

k = 2744*(1mm)³ = 2744mm³. 

Now we know what k is we can answer the question, we substitute the value for k and r = 1.4mm into the equation and solve :

n = 2744mm³/(1.4mm)³ = 1000. Note how the units cancel out which is a good sign we've done things correctly. 

So with a radious of 1.4mm we can make 1000 balls.