The cost of painting the circular traffic sign shown below is $3.50 per square foot. How much to the nearest dollar, will it cost to paint the sign if its diameter measures 36 inches?
Accepted Solution
A:
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 = $0.025then;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.