Question

How much will it cost to paint a circular sign with a radius of 4 feet if the painter charges $\$ 1.50$ per square foot?

Answer 1

Hint: In order to determine the total charges for the painter, first find the total area of the circular sign which is to paint by using the formula of area of circle as $\pi {r^2}$ where $r$ is the radius. Multiply the given area with the charges of the painter for per square foot to get the required result.

Complete step by step solution:
We are given a word problem and form this we have to form some mathematical expression to get the answer.
According to the question, we have to paint a circular sign of radius 4 feet
Lets first find out the total area of the sign which we have to paint.
Since, the sign is a circular sign ,we will be using the formula of area circle to find the total area to paint.
As we know , Area of Circle $ = \pi {r^2}$,where $r$is the radius of the circle and $\pi $is constant value.
Putting radius $r = 4\,ft$in the formula , we get the total area equal to
Area of Circle$ = \pi {\left( 4 \right)^2}$ value of $\pi = 3.14$
$
   = \left( {3.14} \right)\left( {16} \right) \\
   = 50.24\,sq.ft \\
$
We are given that the rate of painter to paint per square foot is $\$ 1.50/sq.ft$
Cost to paint $1\,sq.ft. = \$ 1.50$
Multiplying both sides of the equation with the total area of the circular sign i.e. $50.24\,sq.ft$, we get
Cost to paint \[50.24\left( {1\,sq.ft.} \right) = 50.24\left( {\$ 1.50} \right)\]
Simplifying the above expression , we got the total cost of the painter as
Cost to paint \[50.24\,sq.ft = \$ \,75.36\]

Therefore the total charges to paint the circular sign of area $50.24\,sq.ft$ is equal to \[\$ \,75.36\]


Additional Information:
Mathematical equation: A Mathematical equation can be defined as the mathematical statement which contains an equal symbol $ = $ in between two algebraic expressions that share the same value.

Note: 1. Read the statement carefully in order to convert them into mathematical expressions.
2.Use proper units for the area of the circle.
3. Questions in which we have to obtain the mathematical expression are known as word problems.
4.Verify your answer by using a calculator.