We are given that a mailbox is in the shape of the following figure.
Note that the figure consists of a and half a . To find the 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
ℓ, width
w, and height
h can be calculated using the following formula.
V=ℓwh
We are given that
ℓ=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 with the
r and height
h can be calculated by the following formula.
V=πr2h
In this case, the radius is
5 inches and the height is
9 inches. We can substitute the height and the radius into the formula and calculate the volume of the cylinder.
V=πr2h
V=π(5)2(9)
V=π(25)(9)
V=π(225)
V=706.858…
V≈706.9
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.
2706.9=353.45
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.
990+353.45=1343.45≈1343.5
Therefore, the volume of the mailbox is about
1343.5 cubic inches.