contestada

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

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

Related Links:https://brainly.com/question/16177070

Otras preguntas