Question

A piece of paper can be made into a cylinder in two ways: by joining the short sides together, or by joining the long sides together12. Which cylinder would hold more? How much more?

Answer 1

The solution is:

Bigger volume the cylinder wich radius is (L/2) and h = WHow much according to the relation L/W Let´s call L and W the dimensions of the piece of paper

Let´s assume that

L > WThe Volume (V) of a cylinder is:V(c) = π×r²×h where r is the radius of the circular base, and h is the height of the cylinderFor the first cylinder (V₁) (the one which h = w then r = (L/2)V₁ = π×(L/2)²×w

For the second cylinder (V₂) ( the one with h = L and r = (W/2)V₂ = π×(W/2)²×LThe relation

V₂/V₁ is:V₂/V₁ = π×(W/2)²×L/π×(L/2)²×wV₂/V₁ = W/LBut L > W then V₂/V₁ < 1 or V₂ < V₁The volume of the first cylinder is bigger than the second one:

n:

Hope this helped :]