Question

The city council plans to build a new water storage tank for the community. The tank is cylindrical with a base diameter of 25 ft. and a height of 30 ft. Draw and label a diagram for the new water tank.

a. Find the volume of the tank in cubic feet

b. If 1 cubic foot of water holds 7.5 gallons, how many gallons can the new tank hold?

Answer 1

a.
`14726.216ft^(3)`

b.
`110446.62gal`

Explanation:

I attach the diagram of the new water tank.

a. In order to find the volume of the tank in cubic feet, we will need to calculate the volume of a cylinder. We know that its base measures
`25ft` and its height is
`30ft`.

The volume ''V'' of a cylinder is :

`V=((\pi D^(2))/(4)).(H)`

Where ''
`D`'' is the diameter of the base and ''
`H`'' is the height of the cylinder.

If we replace all the data in the equation :

`V=(\pi .(25ft)^(2))/(4).(30ft)=14726.216ft^(3)`

We found out that the volume of the tank in cubic feet is
`14726.216ft^(3)`

b. We know that 1 cubic foot of water is equal to 7.5 gallons. To find the amount of gallons that the new tank can hold, we need to do an unit conversion.

This equivalence is given to us :

`1ft^(3)=7.5gal` ⇒ Using the equivalence ⇒

`(14726.216ft^(3)).((7.5gal)/(1ft^(3)))=110446.62gal`

Finally, the new tank will hold
`110446.62gal` of water.