How is the formula for the volume of a cylinder derived? A rectangular prism and a cylinder. The rectangular prism is on the left. The width of the prism is pi r, the length is r, and the height is h. The cylinder is on the right. The radius is r and the height is h. Drag and drop the correct word into each box to complete the explanation. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. The rectangular prism and the cylinder have equal heights. The area of the base of the rectangular prism and every cross section parallel to its base is πr2. The area of the base of the cylinder and every cross section parallel to its base is Response area. By Cavalieri's principle, this rectangular prism and this cylinder have Response area volumes. The volume of the rectangular prism is πr2h. Therefore, the volume of the cylinder is πr2h.