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 shave.
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2
(1)
volume of cylinder = πr²h
= (22/7) * 3² * 5
= (22/7) * 45
= 990/7 cm³
(ii)
Volume of Conical hole = 1/3 πr²h
= 1/3 * (22/7) * (3/2)² * (8/9)
= (44/21) cm³
Metal left in the cylinder:
= (990/7) - (44/21)
= 418/3 cm³
Now,
Ratio of volume of metal lift : volume of metal taken out =
(418/3) * (21/44)
= 133/2
= 133 : 2
Hope this helps!
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1
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