The cost of painting the circular traffic sign s̶h̶o̶w̶n̶ ̶b̶e̶l̶o̶w̶ 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?
A: $20
B: $25
C: $30
D: $35
All you need to do is find the how many square feet are in the sign, aka find the area of the sign. The sign is a circle. The area of a circle is πr2. The radius is half the diameter. The diameter is 36 inches. Let's convert that to feet since the price is given in price per square foot. That means the diameter is 36/12 feet, or 3 feet. So the radius is 1.5 feet.
Area of the sign = π(1.5)2
=2.25π square feet
Which is approximately 7.07 square feet.
It costs $3.50 per square foot, and the sign has 7.07 square feet. So it will cost $3.50 * 7.07 total to make the sign.
That is about $24.75
To the nearest dollar, that is $25. So B, $25.
