A cubic meter of water weighs 1000kg. What is the weight of a waterbed mattress that is 1,5 meters by 2 meters by 30 centimetre if the casing of the mattress weighs 1 kg?
To find the weight of the waterbed mattress, we first need to calculate the volume of water it can hold.
The volume of a rectangular prism is given by the formula V = length x width x height.
Converting the height from centimeters to meters, we have: 30 cm = 0.3 m.
So the volume of the mattress is V = 1.5 m x 2 m x 0.3 m = 0.9 cubic meters.
Since 1 cubic meter of water weighs 1000 kg, the weight of the water in the mattress is 0.9 m^3 x 1000 kg/m^3 = 900 kg.
Adding the weight of the casing, the total weight of the waterbed mattress is 900 kg + 1 kg = 901 kg.
To find the weight of the waterbed mattress, we need to calculate the volume of water it can hold and then multiply it by the density of water.
1. First, let's find the volume of the mattress in cubic meters.
The dimensions are given as 1.5 meters by 2 meters by 0.30 meters.
Volume = Length x Width x Height
= 1.5 m x 2 m x 0.30 m
= 0.9 cubic meters
2. Now, let's find the weight of the water in the mattress using the density of water.
Density of water = 1000 kg/cubic meter (given)
Weight of water = Volume x Density
= 0.9 m^3 x 1000 kg/m^3
= 900 kg
3. Finally, let's find the total weight of the waterbed mattress by adding the weight of the casing.
Total weight = Weight of water + Weight of casing
= 900 kg + 1 kg
= 901 kg
Therefore, the weight of the waterbed mattress, including the casing, is 901 kg.
To find the weight of the waterbed mattress, we need to calculate the volume of water it contains and then multiply it by the weight of water per cubic meter.
First, let's calculate the volume of the mattress by multiplying its dimensions:
Volume = Length x Width x Height
Given:
Length = 1.5 meters
Width = 2 meters
Height = 30 centimeters = 0.3 meters
Volume = 1.5 m x 2 m x 0.3 m
Volume = 0.9 cubic meters
Next, we multiply the volume by the weight of water per cubic meter:
Weight = Volume x Weight per cubic meter
Weight per cubic meter of water = 1000 kg/m³
Weight = 0.9 cubic meters x 1000 kg/m³
Weight = 900 kg
However, we need to take the weight of the casing into account. Subtract the weight of the casing from the total weight:
Total weight = Weight of mattress - Weight of casing
Given:
Weight of casing = 1 kg
Total weight = 900 kg - 1 kg
Total weight = 899 kg
Therefore, the weight of the waterbed mattress is 899 kg.