Question

The diagram shows a field. Find the cost of fertilizing the entire field at $0.50 per square yard.
A.



$3360.95


B.



$5853.81


C.



$2095.95


D.



$2945.48

Answer 1

All you need to do is compute the total area of the field, and multiply that by $0.50.
Here we have three shapes to look at:
1) The rectangle in the center with a width of 110 yards and a height of 46 yards.
2) The semicircle to the left side of the field with a diameter of 46 yards.
3) The semicircle identical to the left semicircle on the right side of the field.
Some important formulas for this problem are the area formulas of rectangles and circles, which are:
Rectangle: Area = width*height
Circle: Area = pi*r^2
Now to find the area of the rectangular portion of the field, it's as simple as plugging in for the width and height, those being the 110 yard and 46 yard values from the image.
Area = 110 yards * 46 yards
Area = 5060 yards^3
The semicircles however are a little bit more difficult.
Think about that semicircle. You're given the diameter of the circle, 46 yards, but what we need to find the area using our equation is the radius. From the properties of a circle, we know that the radius is one half the diameter, so our radius is 23 yards.
But before we plug that into our area equation, we also need to realize that we are actually trying to find the area of one half of a circle (in this example, we'll double the area of this semicircle to get the area enclosed by both semicircles, but your other problems may not be so nice to set it up that way).
Area = pi * 23^2 * (1/2) [Remember to stick that one half on there because we're looking at the area of half of a circle!]
Area = 264.5 * pi yards^3
For this problem, we will just double that area to get the area of both of the semicircles on the field.
Area = 529 * pi yards^3
Now add both of our areas:
Total area = 5060 + 529 * pi
Total area is about 6721.902514 yards^3
Multiply that total area by our cost per square foot for fertilizer and you'll have your final answer.
6721.902514 * $0.50
$3360.95

It costs $3360.95 to fertilize the whole field.

Answer 2

oh wow, thank you so much!!