Answer:
Use conversion:
1 square foot = 144 square inches.
As per the statement:
The cost of painting a circular traffic sign is $3.50 per square foot.
⇒Cost of painting a traffic sign = $0.025 square inches.
It is also given that: Diameter measures 36 inches.
Area of a circle is given by:
[tex]A = \pi r^2[/tex]
where r is the radius of the circle.
Diameter = 2r
⇒[tex]36 = 2r[/tex]
Divide both sides by 2 we get;
[tex]r = 18 inches[/tex]
then;
[tex]A = \pi (18)^2 = 3.14 \cdot 324 = 1,017.36[/tex] square inches.
1 square inches = $0.025
then;
In 1,017.36 square inches = [tex]0.025 \cdot 1,017.36 = \$24.7275[/tex]
Therefore, $25 ( to the nearest dollar) will it cost to paint the sign if its diameter measure 36 inches.
