Question

Juan needs a right cylindrical storage tank that holds between

110 and 115 cubic feet of water.
Using whole numbers only, provide the radius and height for 3
different tanks that hold between 110 and 115 cubic feet of
water.
Tank #1
Tank #2
Tank #3
radius =
ft.
radius =
ft.
radius =
ft
height =
ft.
height =
height =
e include the radius and height for each of the three tanks and the
e volume of a cylinder in your answer.​

Answer 1

tank #1:
`r=2\ ft, h=9\ ft,V=113.04\ ft^3`

tank #2:
`r=3\ ft, h=4\ ft,V=113.04\ ft^3`

tank #3:
`r=4\ ft, h=2\ ft,V=100.48\ ft^3`

Explanation:

we know that

The volume of a right cylindrical storage is given by the formula

`V=\pi r^(2)h`

we have that

Juan needs a right cylindrical storage tank that holds between

110 and 115 cubic feet of water

so

For the maximum volume

`115=(3.14)r^(2)h\\36.62=r^(2)h` ----> equation A

For the minimum volume

`110=(3.14)r^(2)h\\35.03=r^(2)h` ____> equation B

Tank # 1

Assume a value for r and then solve for h

For r=2 ft

using equation A

substitute

`36.62=(2)^(2)h`

solve for h

`h=36.62/4\\h=9.2\ ft`

Remember that are whole numbers

so

`h=9\ ft\\r=2\ ft`

Verify the volume

`V=(3.14)(2)^(2)(9)=113.04\ ft^3`

`110 \leq 113.04 \leq 115` ----> is ok

Tank # 2

Assume a value for r and then solve for h

For r=3 ft

using equation B

substitute

`35.03=(3)^(2)h`

solve for h

`h=35.03/9\\h=3.9\ ft`

Remember that are whole numbers

so

`h=4\ ft\\r=3\ ft`

Verify the volume

`V=(3.14)(3)^(2)(4)=113.04\ ft^3`

`110 \leq 113.04 \leq 115` ----> is ok

Tank # 3

Assume a value for r and then solve for h

For r=4 ft

using equation A

substitute

`36.62=(4)^(2)h`

solve for h

`h=36.62/16\\h=2.3\ ft`

Remember that are whole numbers

so

`h=2\ ft\\r=4\ ft`

Verify the volume

`V=(3.14)(4)^(2)(2)=100.48\ ft^3`

`110 \leq 100.48 \leq 115` ----> is ok