Question

A water tank has a diameter of 15 ft and is 22 ft high. a. What is the volume of the tank in ft?? b. In m?? c. In cm?

Answer 1

a)
`V = 3887.72 ft^(3)`

b)
`V = 104.97 m^(3)`

c)
`V = 104,968,468.538 cm^(3)`

Explanation:

A tank has the format of a cylinder.

The volume of the cylinder is given by:

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

In which r is the radius and h is the heigth.

The problem states that the diameter is measured to be 15.00 ft. The radius is half the diameter. So, for this tank

`r = (15)/(2) = 7.50` ft

The height of the tank is 22 ft, so
`h = 22`.

a) Volume of the tank in
`ft^(3)`:

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

`V = pi*(7.5)^2*22`

`V = 3887.72 ft^(3)`

b) Volume of the tank in
`m^(3)`:

We must convert both the radius and the height to m.

Each feet has 0.30 m, so:

Radius:

1 feet - 0.30m

7.5 feet - r m

`r = 7.5*0.30`

`r = 2.25m`

Height

1 feet - 0.30m

22f - h m

`h = 22*0.30`

`r = 6.60m`

The volume is:

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

`V = pi*(2.25)^2*6.60`

`V = 104.97 m^(3)`

c) Volume of the tank in
`cm^(3)`:

Each m has 100 cm.

So
`r = 2.25m = 225cm`

`h = 6.60m = 660cm`

The volume is:

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

`V = pi*(225)^2*660`

`V = 104,968,468.538 cm^(3)`