Question

The cost of painting a circular traffic sign is $2.50 per square foot how much rounded to the nearest cent will it cost to paint the sign if its diameter measures 24 inches?

Answer 1

$94.29 (nearest cents)

Explanation:

Given:

The cost of painting a circular traffic sign is $2.50 per square foot.

Diameter measures 24 inches.

Question asked:

How much rounded to the nearest cent will it cost to paint the sign?

Solution:

First of all we will calculate the area of circular sign and then its cost:-

Diameter = 24 inches

Radius, r =
`(Diameter)/(2) =(24)/(2) =12\ inches`

`Area\ of\ circle=\pi r^(2)`

`=(22)/(7) *(12)^(2) \\ \\ =(22)/(7) *144\\ \\ =(3168)/(7) \\ \\ =452.57\ square\ inches`

By unitary method:

Cost of paint for 1 square foot = $2.50

As we know that 1 foot = 12 inches

Cost of paint for 12 square inches = $2.50

Cost of paint for 1 square inches =
`(2.5)/(12)`

Cost of paint for 452.57 square inches =

`(2.5)/(12)*452.57=(1131.425)/(12) =94.285`

Cost of painting a circular traffic sign will be $94.29 (nearest cents)