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

A half-cylinder is positioned on a rectangular prism with dimensions of 10 inches in width, 9 inches in length, and 11 inches in height. The half-cylinder has a height of 9 inches and a semicircular base with a 5-inch radius.

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

ℓ,

width

w,

and height

h

can be calculated using the following formula.

V = ℓ w h

We are given that

ℓ = 9,

w = 10,

and

h = 11,

so we have enough information to calculate the volume of the rectangular prism.

V = ℓ w h

SubstituteValues

Substitute values

V = 9 (10) (11)

Multiply

V = 990

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.

V = π r^{2} h

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 = π r^{2} h

SubstituteII

$r = 5$ , $h = 9$

V = π (5)^{2} (9)

▼

Simplify right-hand side

CalcPow

Calculate power

V = π (25) (9)

Multiply

V = π (225)

UseCalc

Use a calculator

V = 706.858 \dots

RoundDec

Round to $1$ decimal place(s)

V \approx 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.

\frac{7 0 6 . 9}{2} = 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 \approx 1343.5

Therefore, the volume of the mailbox is about

1343.5

cubic inches.

Exercise