a The circle should touch the sides of one dimension in our rectangular yard.
B
b To calculate the volume, we have to multiply the area of the rectangular backyard that is not part of the pool by the depth expressed in feet.
A
a 15 ft
B
b About $1264
Practice makes perfect
a We know that Lilia's yard is rectangular, with a length of 50 feet and a width of 30 feet. The largest possible circular pool we can fit inside this area will have a diameter that is equal to its width.
If the diameter is 30 feet, the radius must be 15 feet.
Diameter/2=Radius ⇒ 30ft/2=15ft
b The cost of putting in the concrete is the volume of the backyard in cubic feet, that is not part of the pool, multiplied by the concrete's price per cubic feet. To do that we must first find this part's base area. This is the area of the rectangular backyard minus the area of the circular pool.
|c|c|c|
[-1em]
Area & Formula & Calculation [0.1em]
[-0.8em]
Backyard &wl & (30)(50)=1500 [0.2em]
[-0.8em]
Pool& π r^2 & π (15)^2= 225π [0.2em]
[-0.8em]
Concrete& wl-π r^2 & 1500-225π [0.2em]
Now that we know the area of the concrete, we need to find the volume. We know that the concrete has a depth of 8 inches.
To calculate the volume, we must multiply the base area with this depth. Before we can do that, we need make sure that the depth has the same unit as the width and length. Let's convert the measurement so that they are all in feet. Since 12 inches equals 1 foot, we get the following unit rate.
1 foot/12 inches
We can multiply the depth by this unit rate to convert it into feet.
Having converted the depth to feet, we can calculate the concrete's volume by multiplying the base area and the depth.
Volume:& (1500-225π)* 2/3≈ 528.76ft^3
Finally, we can calculate the price of the concrete by multiplying this by the cost per cubic foot.
Price:& 528.76* 2.39≈ $1264
