Exercise 14 Page 595

We are given that a mailbox is in the shape of the following figure.

Note that the figure consists of a rectangular prism and half a cylinder. To find the volume of the mailbox, we need to find the volumes of these two figures. We will start with the 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 $\ell =9,$ $w=10,$ and $h=11,$ so we have enough information to calculate the volume of the rectangular prism. The volume of the rectangular prism is $990$ cubic inches. Next, we will find the volume of the upper figure that is half a cylinder. To do so, we will calculate the volume of the cylinder and divide it by $2.$ Let's start by recalling that the volume of a cylinder with the radius $r$ and height $h$ can be calculated by the following formula. In this case, the radius is $5$ $\text{inches}$ and the height is $9$ $\text{inches}.$ We can substitute the height and the radius into the formula and calculate the volume of the cylinder. The volume of the upper figure is half the volume of the cylinder with the radius of $5$ inches and the height of $9$ inches. Therefore, the volume of the upper figure is about $353.45$ cubic inches. Finally, we can calculate the volume of the mailbox by adding the volume of the prism and the volume of the upper figure. Therefore, the volume of the mailbox is about $1343.5$ cubic inches.