The bottom area of a cylinder and a cone is equal. The ratio of height is 3:5. The volume of a cylinder is 54 cubic centimeters. What is the volume of a cone? Our class teacher said 90, not 30. How can I persuade him?

The bottom area of a cylinder and a cone is equal. The ratio of height is 3:5. The volume of a cylinder is 54 cubic centimeters. What is the volume of a cone? Our class teacher said 90, not 30. How can I persuade him?

Let the volume of the cone be x cubic centimeter, and the area of the bottom of the cylinder and the cone be equal to y
The volume of the cylinder is 54 cubic centimeters
The height of the cylinder is 54 / y
The height of the cone is 3x / y
54/Y：3X/Y=3：5
54：3X=3：5
We can get x = 54 * 5 / 3 / 3 = 30