The radius of the base of a right circular cylinder is halved and the height is doubled. What is the ratio of the volume of the new cylinder to that of the volume of the original cylinder?
Answers
Answered by
276
Original Cylinder
Radius = r
Height = h
Volume = 3.14 * r * r * h
New Cylinder
Radius = r/2
Height = 2h
Volume = 3.14 * r/2 * r/2 * 2h
Therefore,
Required Ratio = New Cylinder : Original Cylinder
= (3.14 * r/2 * r/2 * 2h) : (3.14 * r * r * h)
= (3.14 * r/2 * r/2 * 2h) / (3.14 * r * r * h)
= 1 / 2
= 1 : 2 (ans)
Radius = r
Height = h
Volume = 3.14 * r * r * h
New Cylinder
Radius = r/2
Height = 2h
Volume = 3.14 * r/2 * r/2 * 2h
Therefore,
Required Ratio = New Cylinder : Original Cylinder
= (3.14 * r/2 * r/2 * 2h) : (3.14 * r * r * h)
= (3.14 * r/2 * r/2 * 2h) / (3.14 * r * r * h)
= 1 / 2
= 1 : 2 (ans)
Answered by
107
let the radius of the base of the right circular cylinder be r and the height be h.
the volume of the cylinder is equal to Pi R squared h
when the radius is halved and the height is doubled
then the volume of the cylinder is equal to π(r/2)²2h
=πr²/4×2h
πr²h/2
so the ratio of the volume of new cylinder to the original cylinder is equal to 1:2
the volume of the cylinder is equal to Pi R squared h
when the radius is halved and the height is doubled
then the volume of the cylinder is equal to π(r/2)²2h
=πr²/4×2h
πr²h/2
so the ratio of the volume of new cylinder to the original cylinder is equal to 1:2
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