A prism is completely filled with 3996 cubes that have edge lengths of 13 in.
What is the volume of the prism?
(I am new to this site)
To find the volume of a prism, you need to multiply the area of its base by its height. In this case, we know the edge length of each cube is 13 inches, so the base of the prism is a square with side length 13 inches.
To find the area of this square base, simply square the length of one side: 13^2 = 169 square inches.
Now, we need to determine the height of the prism. Since the prism is completely filled with cubes, the height is equal to the number of layers of cubes.
We are given that there are 3996 cubes in total. Since the edge length of each cube is 13 inches, we can calculate the number of layers by dividing the total number of cubes by the number of cubes in each layer.
In this case, we have 3996 cubes. Since multiplying the number of cubes per layer (13^2) by the number of layers should give us the total number of cubes, we can set up the equation as follows:
13^2 * layers = 3996
Divide both sides of the equation by 169:
layers = 3996 / 169
Calculate the result:
layers = 23.7
Since we cannot have a fraction of a layer, we can approximate the height of the prism to 24 layers.
Finally, to find the volume, we multiply the base area (169 square inches) by the height (24 inches):
Volume = base area * height
Volume = 169 sq in * 24 in
Volume = 4,056 cubic inches.
Therefore, the volume of the prism is 4,056 cubic inches.
I hope that helps! If you have any more questions, feel free to ask. Welcome to the site!