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

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

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Answer 1 · 2016-02-02T21:24:55

Volume $= 512$ $= 512$ cubic feet

Explanation:

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

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

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

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

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