Problem Solving

151. A large right cylinder's height and diameter are given. Then put some little cylinders into it, occupying 80% of its volume. At most how many little cylinders can be put into the large cylinder?
1). Given small cylinder's height and radius
2). Volume of the little cylinder is given.

IMO [spoiler]A[/spoiler]

Should be D IMO.

Either option gives you the volume of the little cylinder.

Even I think it should be A. Only volume is not enough to place a cylinder within another cylinder. Hence we should discard B.

Volume of a cylinder = pi * r^2 * h. So, you can have a smaller volume with higher value for radius than the bigger volume cylinder. Then, even though volume is less you can't fit them in.

E.g: Consider a really long "narrow" cylindrical tube. Now, consider a tin box (Tuna box , Jam box). Even though this tin box has much less volume, you can't fit it inside a narrow tube.

enniguy wrote:Even I think it should be A. Only volume is not enough to place a cylinder within another cylinder. Hence we should discard B.

Volume of a cylinder = pi * r^2 * h. So, you can have a smaller volume with higher value for radius than the bigger volume cylinder. Then, even though volume is less you can't fit them in.

E.g: Consider a really long "narrow" cylindrical tube. Now, consider a tin box (Tuna box , Jam box). Even though this tin box has much less volume, you can't fit it inside a narrow tube.

It should be D because with either of the statements

V big cylinder (80/100) / volume of little cylinder = n

It is true that in the second statement we don't need the 2 pi but even if we have it we can always divide the volume of the smaller one by 2pi.. we'll still get n..

Vote IMO for A.

you need the specific dimensions of the cylinder in order to determine if it "fits"

OA?

IMO A
just volume does not show how it is distributed in cylinder, most aling the length or large diameter & small height....do not ger confused by term "Large"