Question

a rectangular solid block of dimensions 20 cm by 15 cm by 10 cm has a cylindrical hole bored through its centre.the mass of the block is now 14.9 kg and the material of the block has a density of 5 g cm(-3).what is the cross-sectional area of the hole in cm(2)?

Answer 1

The block... without the hole... "should have" a mass of 20cm x 15cm x 10cm x 5 g/cc. 
It "should" have a mass of 15,000 g. 
It doesn't. It has, instead, a mass of 14,900 g. The hole must have removed the missing 100 g. 
Since the density is 5 g/cc, the volume of the hole be 20 cc. 
Volume of a cylinder = Pi x r^2 x height. 

Here's the problem: The height of the cylinder... that is, the length of the hole depends upon what surface of the block was drilled. The hole could be 10, 15 or 20 cm long. 

Volume of the hole = 100 cc = Pi x r^2 x height. We know that the "Pi x r^2" = Area of the base... the area we are looking for. 

So, figure out the orientation of the hole and its length. Divide 100 by the length. That's the answer you are looking for.