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?

The cost of painting the circular traffic sign is given as 3.50 dollar per square feet. The diameter of the traffic sign is 36 inch, then its radius will be [tex]\frac{36}{2} = 18[/tex] inches.

But as the cost is given in unit of feet, we have to convert the radius from inches to feet.

1 inches = 0.0833 feet

18 inches = 18 × 0.0833 feet

So, the radius of the traffic sign will be approximately equal to 1.5 feet.

The area of the traffic sign will be [tex]\pi r^{2} = 3.14 \times 1.5 \times 1.5 = 7.065[/tex] square feet.

So, if the cost of painting 1 square feet of traffic sign is 3.50 dollar, then

cost of painting 7.065 square feet of traffic sign = 3.50 × 7.065 = 24.7 dollar.

Thus, the cost of painting the traffic sign of 7.065 square feet is approximately equal to 25 dollar.