A metallic cylinder has radius 3cm and height 5cm.To reduce its weight, a conical hole is drilled in the cylinder.The conical hole has a radius of 3/2 cm and its depth is 8/9cm. calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.



Ok, here's what you want.
the metallic cylinder's specifications are here.
r₁=3 cm
h₁=5 cm

Now we know that the conical hole is also cylindrical, and the height of it is 8/9 cms and the radius is 3/2 cms. 

so, for the hole...
r₂=3/2=1.5 cm
h₂=8/9 cm

then let's find the area of the metallic cylinder, which is πr₁²h
so, πr₁²h₁= (22/7) (3)² (5)
           A₁ =141.428
           A₁ ≈141.43 cm²

and for the hole....
 πr₂²h₂= (22/7) (1.5)² (8/9)
      A₂ = 6.2857
      A₂ ≈ 6.29 cm²

all we have to do is to conclude the volume of the hole from the cylinder , and that is...
=141.43 - 6.29 
=135.14 cm

Hope it helped. ^_^