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.

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Answers

2016-03-18T20:35:53+05:30
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...
A₁-A₂
=141.43 - 6.29 
=135.14 cm
²

Hope it helped. ^_^

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