A prism is completely filled with 96 cubes that have edge length of 12 cm.
What is the volume of the prism?
the answer is 12
96*12^3 = 165888 cm^3
To find the volume of the prism, we need to multiply the length, width, and height of the prism.
Since the prism is completely filled with cubes, we can assume that the cubes fit perfectly and there are no gaps between them.
We are given that the edge length of each cube is 12 cm. This means that the length, width, and height of the prism are all multiples of 12 cm.
Let's assume the length of the prism is L cubes, the width is W cubes, and the height is H cubes.
Therefore, the volume of the prism can be expressed as:
Volume = L * W * H
Since the prism is completely filled with 96 cubes, we can express this as:
96 = L * W * H
To find the possible combinations of L, W, and H, we can factorize 96:
96 = 2^5 * 3
Now, we need to find the factors of 96 that are multiples of 12. By doing some calculations, we find:
L = 8, W = 4, H = 3
Now, we can substitute these values into the volume formula:
Volume = L * W * H
= 8 * 4 * 3
= 96 * 3
= 288
Therefore, the volume of the prism is 288 cm³.
To find the volume of the prism, we need to calculate the total volume of all the cubes inside it.
The edge length of each cube is given as 12 cm, which means the volume of each cube is calculated by multiplying the edge length by itself twice (a cube has equal length, width, and height).
So, the volume of each cube is 12 cm × 12 cm × 12 cm = 1728 cm³.
Since there are 96 cubes inside the prism, we can multiply the volume of each cube by the total number of cubes to find the total volume of all the cubes combined.
Total volume = Volume of each cube × Number of cubes
= 1728 cm³ × 96
= 165888 cm³
Therefore, the volume of the prism is 165,888 cm³.