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

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:

`A = \pi r^2`

where r is the radius of the circle.

Diameter = 2r

⇒
`36 = 2r`

Divide both sides by 2 we get;

`r = 18 inches`

then;

`A = \pi (18)^2 = 3.14 \cdot 324 = 1,017.36` square inches.

1 square inches = $0.025

then;

In 1,017.36 square inches =
`0.025 \cdot 1,017.36 = \$24.7275`

Therefore, $25 ( to the nearest dollar) will it cost to paint the sign if its diameter measure 36 inches.