Question

A swimming pool is circular with a 20-ft diameter. The depth is constant along east-west lines and increases linearly from 1 ft at the south end to 6 ft at the north end. Find the volume of water in the pool. (Round your answer to the nearest whole number.) ft3

Answer 1

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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Answer 2

`1100 \text{feet}^3`

Explanation:

GIVEN: A swimming pool is circular with a
`20\text{ feet}` diameter. The depth is constant along east-west lines and increases linearly from
`1\text{ feet}` at the south end to
`6\text{ feet}` 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
`=\frac{\text{diameter}}{2}=(20)/(2)=10\text{ feet}`

height of new cylinder
`=6+1=7\text{ feet}`

volume of cylinder
`=\pi r^2h=(22)/(7)*(10)^27`

`=2200\text{ feet}^3`

Volume of swimming pool
`=\frac{\text{volume of cylinder}}{2}=(2200)/(2)`

`=1100\text{ feet}^3`

Hence volume of water in the pool is
`1100 \text{feet}^3`.