Question

If the height of a cylinder is halved, its volume becomes how many times. 


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Answer 1

$\huge\bold\green{Answer}$

Volume of right circular cylinder is directly proportional to its height, and also to square of radius of base. If height is halved, and radius of base remain constant, then volume will also halve......☺

Answer 2

Given : The height of a cylinder is halved.

To find : The change in the volume of the cylinder.

Solution :

The volume of the cylinder will be also halved.

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the change in the volume of the cylinder)

Let,

The base radius of the first cylinder = r unit

The height of the first cylinder = h unit

The volume of the first cylinder = πr²h unit³

Now,

The base radius of the second cylinder = r unit

The height of the second cylinder = h/2 unit (halved)

The volume of the second cylinder = πr²h/2 unit³

Now,

The number of times that the volume of second cylinder is than the volume of first cylinder = Volume of second cylinder ÷ Volume of first cylinder = (πr²h/2) ÷ (πr²h) = (πr²h/2) × (1/πr²h) = ½ times

Which implies, the volume of the second cylinder (or, the cylinder with halved height) is half of the volume of the first cylinder.

Hence, the volume of the cylinder will be also halved.