A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i.e., which figure’s volume increases by a larger factor)? Justify your answer. Write “pi” for and “r^2” for .

Question

A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i.e., which figure’s volume increases by a larger factor)? Justify your answer. Write “pi” for  and “r^2” for .