Answer:
The area needed to be painted is approximately 301.44 square inches.
Step-by-step explanation:
The shape of a donut is represented by two concentrical circles, whose area is described by the following formula:
[tex]A =A_{g}-A_{s}[/tex] (Eq. 1)
Where:
[tex]A[/tex] - Total area of the donut, measured in squared inches.
[tex]A_{g}[/tex] - Area of the greater circle, measured in square inches.
[tex]A_{l}[/tex] - Area of the lesser circle, measured in square inches.
By using the definition of the area of the circle, we expand the equation above:
[tex]A = \frac{\pi}{4}\cdot D^{2}_{ext} - A_{s}[/tex] (Eq. 1b)
If we know that [tex]\pi = 3.14[/tex], [tex]D_{ext} = 22\,in[/tex] and [tex]A_{s} = 78.5\,in^{2}[/tex], the area needed to be painted is:
[tex]A = \frac{(3.14)\cdot (22\,in)^{2}}{4}-78.5\,in^{2}[/tex]
[tex]A \approx 301.44\,in^{2}[/tex]
The area needed to be painted is approximately 301.44 square inches.
