4. The dimensions of a king-size waterbed are 2.1m, 1.8m, and 23 cm. Find the volume and mass of the water it contains when full.
The mattress is shaped, more or less, like a rectangular prism. Use that formula for the volume.
Multiply the three numbers together (with the thickness in meters, not cm), to get the volume in cubic meters.
Then multiply the volume by the density of water, which is 1000 kg/m^3
That will give you the mass of the water in the mattress. The water will weigh much more than the mattress cover that contains it.
To calculate the volume of the waterbed, we need to multiply its dimensions: length, width, and height. The dimensions are given as 2.1m, 1.8m, and 23 cm.
First, we need to convert the height dimension to meters, as the other dimensions are given in meters. Since 1 meter equals 100 cm, we can convert 23 cm to meters by dividing it by 100: 23 cm ÷ 100 = 0.23 m.
Now we have all the dimensions in meters: length = 2.1 m, width = 1.8 m, and height = 0.23 m.
To calculate the volume, we multiply the length, width, and height: volume = length × width × height.
Therefore, the volume of the waterbed is: volume = 2.1 m × 1.8 m × 0.23 m = 0.8796 cubic meters.
To calculate the mass of the water, we need to know the density of water. The density of pure water is approximately 1000 kg per cubic meter.
So, to find the mass of the water in the bed, we multiply the volume by the density: mass = volume × density.
Substituting the values, the mass of the water in the bed is: mass = 0.8796 cubic meters × 1000 kg/cubic meter = 879.6 kg.
Therefore, when the king-size waterbed is full, it contains approximately 0.8796 cubic meters of water and has a mass of 879.6 kilograms.