Math word problem

Question

A museum groundkeeper is creating a semicircular statuary garden with a diameter of 30 feet. There will be a fence around the garden. The fencing cost $9.25 per linear foot. About how much will the fencing cost altogether?

Answer 1

Circumference of a circle= ΠD where D is the diameter of the circle

 

The fencing should cost $9.25 * Π *30

 

There is no specification on the angular width of the semicircular garden.

Answer 2

The perimeter would be the length of the semicircunference + the length of the diameter

P= Length of semicirc  + D         Where D is the diameter and P is                                                           the Perimeter

P=        Π x D             + D         Note: The length of a circle  is ΠxD,  

                2                               but we have a semicircunference                                                           so we have to divide it by 2                                                                                                                                

 

P=    3.14 x 30            +30

               2                      

 

P=     77.10 foot

 

Cost= 77.10 foot x $ 9.25= 713.17   ANSWER   

Answer 3

Recognize that the fencing will encompass an area

that is made up of a curved arc that is half of a

circle plus a straight portion that is the diameter.  

We will be adding the arc length plus the diameter

to get the total perimeter of the garden.

 

d=30 feet...........diameter of circle

θ=180º...............central angle of a semicircle

A=(θº/360º)πd...arc length of a sector

P..........................total perimeter

 

So let's write our equation for total perimeter...

    P=A+d..................................total perimeter equals 

                                                  arc length plus diameter

      =(θº/360º)πd + 30

      =(180/360)(3.14)(30) + 30...substitute for variables

      =(1/2)(3.14)(30) + 30...........simplify

      =47.12 + 30

∴ P=77.12 feet

 

Now let's calculate the total fencing cost...

    $TOT=P x ($cost per foot)

              =77.12 x $9.25

∴ $TOT=$713.40