## Two Similar Cylinders

March 5th, 2008 . by Vanaja

The two cylindrical pans are similar. The diameter of the smaller pan is equal to the radius of the larger pan. How many of these smaller cans could fill the larger can?

**Hint:** Since the two cylinders are similar, their dimensions are in the same ratio. It is given that the diameter of the smaller pan is same as the radius of the larger pan. That is the radius of the two pans are in the ratio 2:1. In other words we can say if the radius of the larger pan is ‘r’ the radius of the smaller pan is r/2 and since they are similar their heights are also in the same ratio 2:1. So, if h is the height of the larger triangle, h/2 is the height of the smaller triangle.

Now,

Volume of the larger cylinder V_{l}= pi r^{2}h

Volume of the smaller cylinder V_{s}=pi(r/2)^{2}(h/2) =(pir^{2}h )/8 = V_{l}/8

i.e V_{s} =V_{l }/8

Therefore 8 smaller pans can fill one larger pan.