Volume of a Cube

[melissamf12]

I need to find the volume of a cube and I know that the formula is v=s^3 but I can not figure out how to solve the equation.
side 1=p^3
side 2=p+7
side 3= p+4
I know my answer is p^5+11p^4+28p^3, but how in the world did I come to this solution?

 

[galactus]

This is not an equation. It is an expression that must be derived by multiplying the length x width x height of the cube.

Just multiply the side lengths together.

\(\displaystyle p^{3}(p+7)(p+4)\)

 

[JeffM]

Technically, you are not dealing with a cube, but rather with a rectangular cuboid.

The formula for the volume of a rectangular cuboid is, as galactus already explained, V = L * W * D where
V = volume,
L = length,
W = width, and
D = depth.

The cube is a special form of rectangular cuboid in which L = W = D.
If we let S = L, then V = L * W * D = S * S * S = S[sup:1238baj0]3[/sup:1238baj0].

 

[Deleted member 4993]

Technically, you are not dealing with a cube, but rather with a rectangular cuboid.

I did not know that term - so I had to Google.

I am so glad this "simplified term" is used now - I was taught "rectangular parallelepiped". I could not ever write that without spell-check.

 

[lookagain]

I need to find the volume of a cube and I know that the formula is v=s^3.

melissamf12,

a side of a cube is a face of a cube. For the volume of a cube,
it is the cube of a length of an edge of the cube.

Where "e" is the length of an edge, the formula for volume is

\(\displaystyle V \ = \ e^3\)

And, if the object is a rectangular cuboid, then its volume is
the product of the lengths of the edges, where the edges
correspond to the dimensions of the length, width, and
height of the cuboid.

 

[mmm4444bot]

I need to find the volume of a cube

side 2 = p + 7

side 3 = p + 4

:idea: These two lengths cannot possibly be equal. This is why the object is not a cube.


I know my answer is p^5+11p^4+28p^3, but how in the world did I come to this solution?

This cannot possibly be your answer, if you don't even know where it came from. :roll: