Question

An architect designs a circular room with a rectangular table inside of it. The diameter of the room is 20 ft, and the table is 10 ft. long and 8 ft. wide. How many square feet in the room will no be occupied by the table?

Answer 1

234.16 square feet

Explanation:

First, let's calculate the total area of the circular room. The formula for the area of a circle is:

`A = \pi r^2`

The diameter of a circle is 2 times the radius, so we can also find area using:

`A = (1)/(4) \pi d^2`

Plugging in our given value for the diameter of the circle, we can calculate the room's area:

`A_(room) = (1)/(4) \pi (20)^2\\A_(room) = 314.16 ft^2`

Next, we will want to calculate the area of the table. Since it is a rectangle, the formula for its area is:

`A = lw`

Plugging in our given values for the table's length and width, we can calculate the table's area:

`A_(table) = (10)(8)\\A_(table) = 80 ft^2`

We are looking for the area of the room that is not occupied by the table. So, we will subtract the area of the table from the area of the room.

`A = A_(room) - A_(table)\\A = 314.16 - 80\\A = 234.16 ft^2`

So, the total area of the room that is not occupied by the table is 234.16 square feet.