there is a glass cylinder and a glass cone with the same height and radius
If the height of the glasses doubled, then the volumes would increase times ___
The volume of a cone is given by the formula V = (1/3)πr^2h and the volume of a cylinder is given by the formula V = πr^2h.
If the height of both the cone and the cylinder is doubled, then the new height would be 2h. Therefore, the new volume of the cone would be (1/3)πr^2(2h) = (2/3)πr^2h and the new volume of the cylinder would be πr^2(2h) = 2πr^2h.
To find out how much the volumes increase by, we need to compare the new volumes to the original volumes.
For the cone: (2/3)πr^2h divided by (1/3)πr^2h = 2/1 = 2
For the cylinder: 2πr^2h divided by πr^2h = 2/1 = 2
Therefore, if the height of the glass cone and glass cylinder is doubled, the volumes would increase by a factor of 2.