Question

Emily is wallpapering a circular room with a ten-foot radius and a height of 8 feet. Ignoring the doors and windows, how much wallpaper will she need?

Answer 1

`160pi` feet or about `502.65` feet.

Here's how I did it:

Explanation:

Since this is a circular room with a height, that means that it is in the shape of a cylinder:

where r is the radius and h is the height.

We also know that you are putting wallpaper around it, meaning that it will go around the room. This is called the lateral area, or the area of all sides of the object excluding the area of the top and the base.
The part colored `color(maroon)("red/maroon")` below shows the lateral area:

Now, let's go on to solving it.

The formula for the lateral area of a cylinder is `2pirh` .
We know that:

• `r` is `10` feet
• `h` is `8` feet

So we can substitute those values into the formula:
`2pi(10)(8)`

And now we simplify:
`2pi80`

`=160pi` feet or about `502.65` feet.

Hope this helps!