Answer :
Answer:
150 pallets.
Step-by-step explanation:
Given:
Dome prep school is planning to plant sod to cover their combined track and football field.
The field is rectangular in the middle, with a width of 160 feet and a length of 360.
On the ends the field is semicircular.
If sod is sold in pallets that will cover 50 square yards each.
Question asked:
How many pallets are needed to cover the entire field ?
Solution:
First of all we will find area of rectangular shape in the middle then of semicircle...
Length = 360 feet
Breadth = 160 feet
[tex]Area\ of\ rectangle=length\times breadth\\[/tex]
[tex]=360\times160=57600\ square\ feet[/tex]
Now, as figure given below, at the end of the field there is a semicircle both sides of breadth, and boundary of breadth is attached to the semicircle the, radius will be half of the breadth:-
Radius = [tex]\frac{160}{2} =80\ feet[/tex]
[tex]Area\ of\ semicircle=\frac{1}{2}\pi r^{2}[/tex]
[tex]=\frac{1}{2} \times\frac{22}{7} \times80\times80=\frac{140800}{14} =10057.142\ square \ feet[/tex]
Total area of two semicircle = 10057.142 square feet (approx)
Combined area of the field = 67657.142 square feet
1 square feet = 0.111 square yard
67657.142 square feet = 67657.142 [tex]\times[/tex] 0.111 = 7517.46 square yard
To calculate number of pallets.
50 square yards = 1 pallets
1 square yards = [tex]\frac{1}{50}[/tex]
7517.46 square yard = [tex]\frac{1}{50}\times7517.46=150.34\\[/tex]
Therefore, about 150 pallets are needed to cover the entire field.