A volume conversion can be difficult to understand if you try to grasp the problem all in one step. Many volume conversion problems give the student a series of linear distances with one set of units, but want the volume in a different set of units. At first glance, this should be a simple conversion problem. The difficulty comes from students not applying the conversion to each of the dimension measurements. This example problem shows a good way to avoid simple errors by trying to accomplish too much in one step. The example is for the cubic feet to liters volume conversion.

### Volume Conversion Example

How many liters of water does it take to fill a swimming pool 11.0 feet by 11.0 feet and 8.00 feet deep?

Given:

1 foot = 12 inches

1 inch = 2.54 centimeters

1 Liter = 10^{3} cm^{3}

### Solution:

Our swimming pool’s measurements are given in feet. We need to convert these measurements into something we can use to find the volume measurement of liters. Looking at the given unit conversions, we can convert feet to inches and then to centimeters.

Start with the 11.0 feet measurement.

11.0 feet = 335 cm

Now the 8.00 feet measurement.

8.00 feet = 243 cm

Now we can multiply these together to get the volume of the swimming pool.

Volume of swimming pool = 11.0 feet ⋅ 11.0 feet ⋅ 8.00 feet

Volume of swimming pool = 335 cm ⋅ 335 cm ⋅ 243 cm

Volume of swimming pool = 27,270,675 cm^{3} = 2.7 × 10^{7} cm^{3}

Now we can use the final conversion to get the volume in liters.

step 6

Volume of swimming pool = 2.7 × 10^{4} Liters

### Answer:

It takes 2.7 × 10^{4} liters of water to fill a swimming pool with dimensions 11′ × 11′ × 8′.

It is a good way to avoid errors by converting each of the linear units before trying to multiply the lengths to get a volume.

I think it would be better to do this way :

V = ( L ) ( W ) ( H ) = ( 11.0 ft ) ( 11.0 ft ) ( 8.00 ft ) = 968 ft^3

V = ( 968 ft^3 ) ( 1.0 m^3 / 35.31 ft^3 ) ( 1000 L / m^3 ) = 27410 L = 2.741 x 10^4 L <———