Question

. Mr. Donut wants to paint a donut on the wall of his restaurant. The diameter of the outside edge of the donut will be 22 inches. The area of the hole of the donut will be 78.5 square inches. How much area will need to be painted if only the donut needs to be painted? Use 3.14 for π.

Answer 1

The area needed to be painted is approximately 301.44 square inches.

Explanation:

The shape of a donut is represented by two concentrical circles, whose area is described by the following formula:

`A =A_(g)-A_(s)` (Eq. 1)

Where:

`A` - Total area of the donut, measured in squared inches.

`A_(g)` - Area of the greater circle, measured in square inches.

`A_(l)` - Area of the lesser circle, measured in square inches.

By using the definition of the area of the circle, we expand the equation above:

`A = (\pi)/(4)\cdot D^(2)_(ext) - A_(s)` (Eq. 1b)

If we know that
`\pi = 3.14`,
`D_(ext) = 22\,in` and
`A_(s) = 78.5\,in^(2)`, the area needed to be painted is:

`A = ((3.14)\cdot (22\,in)^(2))/(4)-78.5\,in^(2)`

`A \approx 301.44\,in^(2)`

The area needed to be painted is approximately 301.44 square inches.