Question

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?

Answer 1

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

Explanation:

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 $\frac{36}{2} = 18$ 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 $\pi r^{2} = 3.14 \times 1.5 \times 1.5 = 7.065$ 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.