The problem asks to find the total length of wallpaper needed to cover the inside surface of an archway. The archway consists of two vertical sides and a semicircle on top. The height of each vertical side is 66 inches, and the radius of the semicircle is 20 inches. We need to find the total length of the two vertical sides plus the length of the semicircle's arc. We are given that $\pi = 3.14$.

1. Problem Description

The problem asks to find the total length of wallpaper needed to cover the inside surface of an archway. The archway consists of two vertical sides and a semicircle on top. The height of each vertical side is 66 inches, and the radius of the semicircle is 20 inches. We need to find the total length of the two vertical sides plus the length of the semicircle's arc. We are given that $\pi = 3.14$.

2. Solution Steps

First, we find the total length of the two vertical sides.

Since each side is 66 inches, the total length of the two sides is $2 \times 66 = 132$ inches.

Next, we find the length of the semicircular arc. The circumference of a full circle is given by the formula:

$C = 2\pi r$

Since we have a semicircle, we need to find half of the circumference:

Semicircle arc length = $\frac{1}{2} \times 2\pi r = \pi r$

The radius $r$ is given as 20 inches, and we are told to use 3.14 for $\pi$.

Semicircle arc length = $3.14 \times 20 = 62.8$ inches.

Finally, we add the length of the two sides and the length of the semicircular arc to find the total length of the wallpaper strip.

Total length = $132 + 62.8 = 194.8$ inches.

We need to round the answer to the nearest inch, which is 195 inches.

3. Final Answer

195 inches