Question

The radius and the height of the cylinder are multiplied by 1/3. what will be the effect on the volume of the cylinder?

Answer 1

okay well for example--if the radius was 6 and the height was 12 the volume would be 1357.17, and if you multiply those by 1/3 which is the same as dividing it by 3, then you would have a radius off 2 and a height of 4, and the volume of that is 50.27, sooooooooo well the volume of the cylinder would decrease by like 26 to 27 times.

Answer 2

The volume is multiplied by 1/27.

Explanation:

Let the radius equal r and the height equal h for the original cylinder.

The volume of a cylinder with radius r and height h is V=πr2h.

Therefore, the volume for the original cylinder is πr2h.

The new cylinder has dimensions that are one third those of the original cylinder: the radius equals 1/3r and the height equals 1/3h.

To calculate the volume of the cylinder, substitute the new values into the formula for volume of a cylinder.

V=π⋅(r3)2⋅(h3)

Simplify.

V=1/27πr2h

The new volume is 1/27πr2h.

If the radius and the height of the cylinder are multiplied by 1/3, the volume is multiplied by 1/27.

Therefore, the new volume is the original volume multiplied by 1/27.