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

Answer:

$94.29 (nearest cents)

Step-by-step 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 = $\frac{Diameter}{2} =\frac{24}{2} =12\ inches$

$Area\ of\ circle=\pi r^{2}$

                       $=\frac{22}{7} \times(12)^{2} \\ \\ =\frac{22}{7} \times144\\ \\ =\frac{3168}{7} \\ \\ =452.57\ square\ inches$

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 = $\frac{2.5}{12}$

Cost of paint for 452.57 square inches =

$\frac{2.5}{12}\times452.57=\frac{1131.425}{12} =94.285$

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