A cubic tank holds 1,000.0 kg of water. What are the dimensions of the tank in meters? Explain your answer.
The volume of a cube of length a (on each side) is a^3.
a^3 = 1000 in this case
Take the cube root of each side.
To find the dimensions of the cubic tank in meters, we need to use the equation for the volume of a cube. The volume of a cube is given by the formula:
Volume = side length³
We know that the mass of water in the cubic tank is 1,000.0 kg. However, we need to convert this mass into the volume of water in cubic meters since the dimensions of the tank are in meters.
To do this, we need to use the density of water, which is approximately 1,000 kg/m³. The density of water tells us that 1 cubic meter of water weighs 1,000 kilograms. So, if we divide the mass of water (1,000.0 kg) by the density of water (1,000 kg/m³), we get the volume of water in cubic meters:
Volume of water = Mass of water / Density of water
= 1,000.0 kg / 1,000 kg/m³
= 1 cubic meter
Since the volume of water equals the volume of the tank, we can now find the side length of the cube by solving for it in the volume equation. Let's call the side length "s":
1 cubic meter = s³
To find the value of "s", we need to take the cubic root of both sides:
s = ∛(1 cubic meter)
The cubic root of 1 cubic meter is simply 1, so the side length of the cube is 1 meter.
Therefore, the dimensions of the tank are 1 meter in length, 1 meter in width, and 1 meter in height.
To find the dimensions of the tank in meters, we need to know the volume of the tank. The volume of a cube is given by the formula V = s^3, where V is the volume and s is the side length of the cube.
Given that the tank holds 1,000.0 kg of water, we can use the fact that 1 liter of water is equal to 1 kg. Therefore, the volume of the tank is 1,000.0 liters.
To convert liters to cubic meters, we must divide by 1,000, since there are 1,000 liters in a cubic meter. Therefore, the volume of the tank is 1,000.0 liters / 1,000 = 1 cubic meter.
Since the tank is a cube, all sides have equal lengths, so the side length of the tank is the cube root of the volume. Therefore, s = ∛1 = 1 meter.
Hence, the dimensions of the tank are 1 meter by 1 meter by 1 meter.
I left out a step. 1000 kg of water has a volume of 1 cubic meter or 10^6 cubic cm.
Write
V = a^3 = 1.000 m^3 and take the cube root of each side
a = 1.000 meter