Video: Solving Problems Involving Density Calculations

A submarine has a volume of 1005 cubic feet. Its density must be less than or equal to 62.43 pounds per cubic foot to float on the surface of the water. What is the greatest possible mass that the submarine could have before sinking?

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Video Transcript

A submarine has a volume of 1005 cubic feet. Its density must be less than or equal to 62.43 pounds per cubic foot to float on the surface of the water. What is the greatest possible mass that the submarine could have before sinking?

First of all, density equals mass over the volume. Our submarine has an unknown mass and a volume of 1005 feet cubed. The density of our submarine, this value, must be less than or equal to 62.43 pounds per cubic foot for every one foot cubed. We can substitute 𝑥 pounds over 1005 feet cubed for the density, like this.

Now that we have this inequality set up, we solve for pounds. We do that by cross multiplying, one foot cubed times 𝑥 pounds. 𝑥 times one must be less than or equal to 1005 feet cubed times 62.43 pounds, 1005 times 62.43. One times 𝑥 equals 𝑥. 𝑥 is less than or equal to 62742.15. Remember that our 𝑥-value is a measurement of pounds. 𝑥 must be less than or equal to 62742.15 pounds.

Now, we’ve set up our problem to tell us how to keep the submarine afloat. Our question is asking what is the greatest possible mass that the submarine can have before it starts to sink. Well, if 𝑥 is equal to this value, it will float. But any more than this and it starts to sink.

𝑥’s greatest possible mass 62742.15 pounds.

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