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?
To find the cost of painting the circular traffic sign, we first need to determine the area of the sign.
1. Convert the diameter from inches to feet:
Since there are 12 inches in a foot, divide 36 inches by 12 to get 3 feet.
2. Find the radius of the sign:
The radius is half of the diameter, so divide 3 feet by 2 to get 1.5 feet.
3. Calculate the area of the sign:
The area of a circle is given by the formula A = πr^2, where r is the radius.
So, the area of the sign is A = π * (1.5 feet)^2.
Using the approximation of π as 3.14, the area is:
A ≈ 3.14 * (1.5 feet)^2.
4. Compute the cost of painting:
The cost is $3.50 per square foot.
Multiply the area of the sign by the cost per square foot:
Cost = (3.14 * (1.5 feet)^2) * $3.50.
Now we can calculate the cost:
Area ≈ 3.14 * (1.5 feet)^2
Area ≈ 3.14 * 2.25 square feet
Area ≈ 7.065 square feet
Cost ≈ 7.065 square feet * $3.50
Cost ≈ $24.73
Therefore, it will cost approximately $24, to the nearest dollar, to paint the sign.
To calculate the cost of painting the circular traffic sign, we first need to find the area of the sign.
The diameter of the sign is given as 36 inches, which means the radius (half the diameter) would be 18 inches.
To convert inches to feet, we divide by 12 since there are 12 inches in a foot: 18 inches ÷ 12 = 1.5 feet.
Next, we need to calculate the area of the circular sign using the formula: Area = π * r^2, where π is approximately 3.14 and r is the radius.
Area = 3.14 * (1.5 feet)^2
Area = 3.14 * 2.25 square feet
Area ≈ 7.065 square feet
Now that we have the area of the sign, we can calculate the cost of painting it. The cost is given as $3.50 per square foot.
Cost = Area * Cost per square foot
Cost = 7.065 square feet * $3.50 per square foot
Cost ≈ $24.75
Therefore, to the nearest dollar, it will cost approximately $25 to paint the circular traffic sign.
A = pi * r^2
A = 3.14 * 1.5^2
A = 7.065 square feet
7.065 * 3.5 = $____________