Elizabeth and Virat use small cubes to make the rectangular prism as show below . The length of each edge of the small cubes is 1/4 centimeter . Elizabeth uses a volume formula to find that the volume of the prism is 1 41/64 cubic centimeters . Virat decides to count the cubes to find the volume of the prism .
how many small cubes with edge length 1/4 cenimeter does it take to make the prism?
1 41/64 = 105 * (1/4)^3
you just have to ay attention
To find the number of small cubes with an edge length of 1/4 centimeter that make up the prism, we need to calculate the volume of the prism using the given information.
Elizabeth has already used a volume formula to find that the volume of the prism is 1 41/64 cubic centimeters. To understand how she arrived at that answer, we can break down the process of finding the volume.
The volume of a rectangular prism is determined by multiplying its length, width, and height. In this case, we are given the volume and need to find the number of small cubes. So, we can work backwards by dividing the volume by the volume of a single small cube.
The volume of a small cube with an edge length of 1/4 centimeter can be calculated using the formula:
Volume = length x width x height
Since all the edges of the small cube are equal, the formula can be simplified to:
Volume = edge length^3
Substituting the values, we get:
Volume of small cube = (1/4 centimeter)^3
Simplifying further:
Volume of small cube = 1/64 cubic centimeters
Now that we know the volume of a single small cube, we can determine the total number of cubes that make up the prism by dividing the volume of the prism by the volume of a single small cube:
Total number of small cubes = Volume of prism / Volume of small cube
Total number of small cubes = (1 41/64 cubic centimeters) / (1/64 cubic centimeters)
To simplify this division, we need to convert 1 41/64 into an improper fraction. Multiplying the whole number (1) by the denominator (64) and adding the numerator (41) gives us:
Total number of small cubes = (105/64) / (1/64)
Finally, dividing the fractions:
Total number of small cubes = 105/64
Therefore, it takes 105 small cubes with an edge length of 1/4 centimeter to make the rectangular prism.