The problem asks to find the total length of wallpaper needed to cover the inside surface of an archway, from the floor on one side, up and over the arch, and down to the floor on the other side. The archway consists of two vertical segments of 66 inches each, and a semi-circle on top with radius 20 inches. We need to use 3.14 for $\pi$ and round the answer to the nearest inch.

1. Problem Description

The problem asks to find the total length of wallpaper needed to cover the inside surface of an archway, from the floor on one side, up and over the arch, and down to the floor on the other side. The archway consists of two vertical segments of 66 inches each, and a semi-circle on top with radius 20 inches. We need to use 3.14 for $\pi$ and round the answer to the nearest inch.

2. Solution Steps

The total length of the wallpaper is the sum of the lengths of the two vertical segments and the length of the semi-circle.

The length of each vertical segment is 66 inches. So, the total length of the two vertical segments is $2 \times 66 = 132$ inches.

The length of a semi-circle is half the circumference of a circle.

The formula for the circumference of a circle is $C = 2 \pi r$, where $r$ is the radius.

The radius of the semi-circle is given as 20 inches.

So the length of the semi-circle is $\frac{1}{2} \times 2 \pi r = \pi r$.

Using $\pi = 3.14$ and $r = 20$ inches, the length of the semi-circle is $3.14 \times 20 = 62.8$ inches.

The total length of the wallpaper is the sum of the lengths of the two vertical segments and the semi-circle:

$132 + 62.8 = 194.8$ inches.

Rounding this to the nearest inch, we get 195 inches.

3. Final Answer

195 inches