The volume of a cube is length*width*height. In a cube all the side lengths are equal. Volume=7cm*7cm*7cm=343cm^3

The volume of a cube is given by multiplying its length, width, and height, which are all equal. Therefore we can say:

Substitute in our given measurement:

We want to know the volume of the cube if it is cut in half, so let's divide this answer in two:

At your university there is a metal cube-shaped sculpture near the math building. If the cube has a side length of 4 meters, what is the cube's volume?

Begin with the formula for volume of a cube, then just simplify:

First, you will want to create a pyramid with measurements that are easy to calculate. So, let's say that we have pyramid with a base edge of 10 inches and a height of 10 inches. 

So the volume of the original pyramid would be equal to 

The volume of the altered pyramid would be equal to:

To find the relationship between the volume of the altered pyramid relative to the volume of the original pyramid, divide the altered volume by the original volume. 

The new volume is 59% of the original volume, which means there was a 41% decrease in volume. 

If the length of one side is 756 ft, then multiply to find the area of the base.

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem. 

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

Add the surface area of the base to the surface area of the four triangles.

Volume of a pyramid is

Thus:

Area of the base is .

Therefore, each side is .

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.  

Since the base is a square, the area of the base is 3 x 3 = 9.  

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

The formula for the area of a pyramid is . In this case, the length is , the width is , and the height is . 

 and . 

To find the volume of a pyramid, you need to use the equation below:

To find the height (shown by the yellow line), we can draw a right triangle using the yellow line, blue line and side b (5 inches). Because the hypotenuse is 5 inches, using the common Pythagorean 3-4-5  triple. The blue line is 3 inches and the yellow line (height) is 4 inches. Also, to find side a, we can use the blue line (3 inches) and half of the red line (3 inches)  and the Pythagorean Theorum.

Because the base is a square, the area of the base is equal to the square of side a:

Now we plug in these values to find the volume:

The volume  of a rectangular pyramid with height , base width , and base length  is given by 

.

For this pyramid, , , and  To calculate its volume, substitute the values for , , and  into the formula:

Therefore, the volume of the given rectangular pyramid is