Answer:
[tex]1100 \text{feet}^3[/tex]
Step-by-step explanation:
GIVEN: A swimming pool is circular with a [tex]20\text{ feet}[/tex] diameter. The depth is constant along east-west lines and increases linearly from [tex]1\text{ feet}[/tex] at the south end to [tex]6\text{ feet}[/tex] at the north end.
TO FIND: Find the volume of water in the pool.
SOLUTION:
Consider the image attached.
when two similar figures are attached a new cylinder is formed. volume of swimming pool is half of volume of new cylinder formed.
radius of new cylinder [tex]=\frac{\text{diameter}}{2}=\frac{20}{2}=10\text{ feet}[/tex]
height of new cylinder [tex]=6+1=7\text{ feet}[/tex]
volume of cylinder [tex]=\pi r^2h=\frac{22}{7}\times(10)^27[/tex]
[tex]=2200\text{ feet}^3[/tex]
Volume of swimming pool [tex]=\frac{\text{volume of cylinder}}{2}=\frac{2200}{2}[/tex]
[tex]=1100\text{ feet}^3[/tex]
Hence volume of water in the pool is [tex]1100 \text{feet}^3[/tex].
The volume of water in the pool is: 1,100.1413ft³
First step is to calculate the volume of the cylinder using this formula
V1=π×(radius)²×height
Where:
radius =20ft/2=10 f t
height=1 f t
Let plug in the formula
V1=π×(10ft)²×1ft²
V1=314.1593ft²
Second step
Let V2 represent the half of the volume of a cylinder with a radius of 10ft and a height of 5ft
V2=0.5×π×(10ft)²×5ft²
V2=785.3982ft²
Third step is to determine the volume of water in the pool using this formula
V=V1+V2
Let plug in the formula
V=314.1593+785.3982
V=1,100.1413ft³
Inconclusion the volume of water in the pool is: 1,100.1413ft³
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