Respuesta :
- The question is which cylinder hold more ( has a bigger volume)
- How much more ( what is the mathematical relation between the volumes of the two cylinders
The solution is:
Bigger volume the cylinder wich radius is (L/2) and h = W
How 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 > W
The 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 cylinder
- For 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×L
The relation V₂/V₁ is:
V₂/V₁ = π×(W/2)²×L/π×(L/2)²×w
V₂/V₁ = W/L
But L > W then V₂/V₁ < 1 or V₂ < V₁
The volume of the first cylinder is bigger than the second one
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