The number of uniform spherical shots that can be made from a given mass of lead varies inversely to the cube of the radius. When the radius is 1mm the number of shots made is 2744. How many shots of radius 1.4mm can be made from the same mass.

The key to long questions like these is picking out the key information quickly.
We have 2 pieces of information we are interested in, the number of shots and the radius of each shot, so let's assign them a letter.
let n = # of shots that can be made
let r = radius of each shot
We know, from the question, the number of shots is inverseley proportional to the radius of each shot. i.e. 
n = k/r³
We see in the equation above that n is equal to some number ( a constant ) divided by r^3. If we could find this constant we would be able to substitute in our radius to find the number of shots.
To find the constant let's substitute in the information we already have
2744 = k/1³
therefor k = 2744
Now it should be easy to get that n to pop out
n = 2744/1.4³
Although you will most likely use a calculator for this last step, write down the calculation anyway so the examiner knows what you have done. 
n = 1000