Exercise 16 Page 595

We are asked to determine which of the given pans will hold more cake batter, the rectangular pan or two round pans. To do so, we need to find the volume of each pan. Let's start with the rectangular pan. Note that this pan is in the shape of a rectangular prism. Recall that the volume of a rectangular prism with length $\ell ,$ width $w,$ and height $h$ can be calculated using the following formula. We are given that $\ell =9,$ $w=13,$ and $h=2,$ so we have enough information to calculate the volume of the rectangular prism. The volume of the rectangular pan is $234$ cubic inches. Next, we will find the volume of the round pan. Notice that this pan is in the shape of a cylinder. The volume of a cylinder with the radius $r$ and height $h$ can be calculated by the following formula. In this case, we are given the diameter and the height of the cylinder. To find the radius we can divide the diameter $d$ by $2.$ We got that the radius of the cylinder is $4$ inches. Now, we can substitute the height and the radius into the formula and calculate the volume of the cylinder. The volume of the round pan is about $101$ cubic inches. Therefore, the volume of two round pans is about $2\cdot 101$ or about $202$ cubic inches. Finally, we can compare the volume of the rectangular pan with the volume of two round pans. We can see that the volume of the rectangular pan is greater than the volume of two round pans. Therefore, the rectangular pan will hold more cake batter than two round pans.