An aquarium in the shape of a rectangular prism dimensions of 4 ft by 2 ft by 2 ft is filled up to 80% capacity with water that has a density of 62 lb/ft^3. Should the aquarium be placed on a table that can support a maximum weight of 600 lbs.

Explain why or why not (using math preferably)

You want to know if a 4' by 2' by 2' aquarium filled 80% with water at 62 lb/ft³ should be placed on a table with a capacity of 600 lb.

Aquarium weight

The weight of the aquarium water will be its volume multiplied by its density. The volume is 80% of the product of the aquarium dimensions, so the weight of the water is ...

(4 ft)(2 ft)(2 ft)(0.80)(62 lbs/ft³) = 793.6 lbs

Comparison

This weight is somewhat greater than the maximum weight the table will support. The aquarium should not be placed on the table.

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Additional comment

If the aquarium were filled to 60% capacity, the weight of the water would be about 595 lb. The table could support that with no safety margin. The weight of the aquarium itself, and any rocks or other decoration placed in it could cause the capacity of the table to be exceeded.

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An aquarium in the shape of a rectangular prism dimensions of 4 ft by 2 ft by 2 ft is filled up to 80% capacity with water that has a density of 62 lb/ft^3. Should the aquarium be placed on a table that can support a maximum weight of 600 lbs. Explain why or why not (using math preferably)

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Aquarium weight

Comparison

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An aquarium in the shape of a rectangular prism dimensions of 4 ft by 2 ft by 2 ft is filled up to 80% capacity with water that has a density of 62 lb/ft^3. Should the aquarium be placed on a table that can support a maximum weight of 600 lbs.

Explain why or why not (using math preferably)