If the surface area of a cube is 384 square feet,what is its volume?

Answer 1

Volume #= 512 # cubic feet

A cube has #6# faces all with equal area. If the total surface area of the cube is #384# sq.ft. then each face has an area of #384div6=64# sq.ft.

Each face of a cube is a square and if we denote the length of an edge as #E# then the area of a face (in this case #64# sq.ft.) is equal to #E^2# #color(white)("XXX")E^2=64# sq.ft. #color(white)("XXX")rarr E = 8# sq.ft.

The volume of a cube with edges of length #E# is #E^3#. In this case #"Volume" = E^3 = 8^3 = 512# sq.ft.

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Answer 2

Noah Atkinson

To find the volume of the cube, you can use the formula: Volume = side length^3.

Given that the surface area of the cube is 384 square feet, you can find the side length by using the formula for the surface area of a cube: Surface Area = 6 * side length^2.

Solving for side length: 384 = 6 * side length^2 => side length^2 = 384 / 6 => side length^2 = 64 => side length = √64 => side length = 8 feet

Now, plug the side length into the formula for volume: Volume = side length^3 Volume = 8^3 Volume = 512 cubic feet.

Therefore, the volume of the cube is 512 cubic feet.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.