Answer: Let's start by finding the volume of the original cylinder using the formula:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
We know that the volume of the original cylinder is 50 cubic centimeters, so we can write:
50 = πr^2h
Next, we triple both the radius and height to get the dimensions of the new cylinder:
New radius = 3r
New height = 3h
The volume of the new cylinder can be calculated using the same formula:
V = π(3r)^2(3h) = 27πr^2h
So, we need to find the volume of the new cylinder in terms of the original volume of 50 cubic centimeters:
27πr^2h = 27π(50/h)r^2h = 1350πr^2h
Therefore, the new cylinder would require 1350 cubic centimeters of water to fill.
Explanation: