How to find the volume of a cube - Math

Vertices = three planes coming together at a point = 8

Edges = two planes coming together to form a line = 12

Faces = one plane as the surface of the solid = 6

Vertices + Edges + Faces = 8 + 12 + 6 = 26

Vcube = s3 = (2x)3 = 8x3

Vsphere = 4/3 πr3 = 4/3•3.14•x3 = 4.18x3

A cubic volume is . Let the original sides be 1, so that the original volume is 1. Then find the volume if the sides measure 5. This new volume is 125. Therefore, the ratio of new volume to old volume is 125: 1.

If we let represent the length of an edge on the smaller cube, its volume is .

The larger cube has edges three times as long, so the length can be represented as . The volume is , which is .

The large cube's volume of is 27 times as large as the small cube's volume of .

When searching for the volume of a cube we are looking for the amount of the space enclosed by the cube.

To find this we must know the formula for the volume of a cube which is

Using this formula we plug in the side length for to get

Cube the side length to arrive at the answer of

The answer is .

To find this we must know the formula for the volume of a cube which is

We plug the volume into the equation yielding

Then we take the cube root of both sides giving us

We now know

The answer is .

Since the dice are on each of their sides, of them would measure in length when standing face-to-face. This means dice will fit along the edge of the box that measures .

dice will also fit on the edge of the box measuring , but will not fit since adding an additional die would bring the length of the dice standing face-to-face up to . There are no half-dice to fill the gap, so there is a small empty space on this side.

dice will fit along the side that measures .

Treating "dice" as the unit of measurement instead of and considering only the volume where the dice will fit, one ends up with a rectangular shape measuring dice dice dice. The volume of this shape is the number of dice that will fit in this area (and thus the box). Find the volume by multiplying all lengths of the shape's sides together:

dice dice.

In order to solve this problem, we need to make sure that the measurements given are in uniform units. In this case, we will use centimeters; therefore, we need to convert the other units of meters and millimeters into centimeters via dimensional analysis.

Solve for the width.

Solve for the height.

Now, solve for volume by using the formula .

If you calculated , then you did not convert into appropriate units.

A few facts need to be known to solve this problem. Observe that the diagonal of the square face of the cube cuts the qradilateral into two right isosceles triangles; therefore, the length of a side of the square to its diagonal is the same as an isosceles right triangle's leg to its hypotenuse: .

Rearrange an solve for .

Now, solve for the volume.

In order to solve this question, we need to convert miles to meters via dimensional analysis and then solve for the volume of the building.

Now, solve for volume.

The volume of a cube is one side cubed. Because we know that one face has an area of 16 in2, then we know that one side must be the square root of 16 or 4. Thus the volume is .

Since a cube has square faces and the surface area of each face is given by multiplying the length of one side of the square face by itself, the equation for the surface area of a cube is , where is the length of one side of one face (i.e., one edge of the cube). Find the length of one side/edge of the given cube by setting the given surface area equal to :

units

The volume of a cube is , where is the length of one of the cube's edges. Substituing the solution to the previous equation for in the volume equation gives the volume of the cube:

units cubed

We only have the length of one edge, but that is sufficient for finding the volume. The volume of a cube equals one edge multiplied by itself three times:

The formula for the volume of a cube is

,

where is the side of the cube.

Plugging in our values, we get:

The formula for the volume of a cube is:

Since the length of one side is meters, the volume of the cube is:

meters cubed.

The formula for the volume of the cube is

Plugging that into Volume equation, we find and

Thus, the answer is 512x6

If we let represent the length of an edge on the smaller cube, its volume is .

The larger cube has edges three times as long, so the length can be represented as . The volume is , which is .

The large cube's volume of is 27 times as large as the small cube's volume of .

The volume of a cube is

So with a side length of 7 inches, the volume is