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A container made of metal is in the shape of a frustum of a cone mounted on a hollow cylindrical base of the same metallic sheet. The diameter of the two circular ends of the container are 50 cm and 36 cm, the total vertical height of the container is 30 cm and that of the cylindrical base is 6 cm. Also, find the volume of milk the container can hold

What I tried:

Diagram: enter image description here

Height of frustum=$30-6=24$ cm

Radius of upper circle=$\dfrac{Diameter}{2}=\dfrac{50}{2}=25$ cm

Similarly radius of lower circular base=$18$ cm

Slant height $l=\sqrt{h^2+(r_1-r_2)^2}$ so $l=25$

Volume of milk $=$ Volume of frustum

My question: Will we include the lower cylinder volume in the total volume of milk container can hold?

Sale Ram
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  • Yes you have to add the lower cylinder volume as it is part of the container. – Math Lover Dec 25 '21 at 16:33
  • @MathLover Then can you please tell why we didn't add volume of lower cylinder in this similar question? – Sale Ram Dec 25 '21 at 16:47
  • because I interpreted differently than the other solution does. – Math Lover Dec 25 '21 at 16:54
  • The question is ill-posed. I have a similar galvanised bucket at home in which the base of the bucket is at the top of the cylinder. Others may have the base at the bottom of the cylinder. Without that information there is no unique solution. – Anton Dec 25 '21 at 16:59

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