A rectangle prism is measured 84cm (L)X 42cm (w) X 56cm (H). What is the largest size cube that fits the dimensions of the prism? What number of cubes is required?
i don't even know how to start it T_T
The question is poorly worded
Interpretation #1
The largest cube to fit into the box is obviously one which measures 42 by 42 by 42 and you can only get one in
Interpretation #2
What is the size of the largest cubes with which I can fill the box
the largest to fill the entire base is a 2 by 2 by 2.
I will let you figure out how many of those will fit in
Based on the given dimensions of the rectangular prism (84cm x 42cm x 56cm), it seems like you want to determine two things: the largest size cube that fits into the prism and the number of cubes required to fill the prism.
To find the largest cube that fits into the prism, you need to identify the dimensions of the cube that are smaller or equal to the corresponding dimensions of the prism.
In this case, the dimensions of the prism are 84cm (length), 42cm (width), and 56cm (height). To find the largest cube, you need to determine the common factor between these dimensions.
The greatest common factor (GCF) of 84, 42, and 56 is 14.
Therefore, the largest cube that fits into the prism will have dimensions of 14cm x 14cm x 14cm.
To determine the number of cubes required to fill the entire prism, you need to calculate the volume of the prism and divide it by the volume of the cube.
The volume of the prism can be calculated using the formula: volume = length x width x height.
In this case, the volume of the prism = 84cm x 42cm x 56cm.
The volume of the cube is calculated using the formula: volume = side length x side length x side length.
In this case, the volume of the cube = 14cm x 14cm x 14cm.
To find the number of cubes required, you can divide the volume of the prism by the volume of the cube.
Number of cubes required = (volume of prism) / (volume of cube)
Please perform the calculations using the given measurements and formulas to find the solution: the largest size cube that fits the dimensions of the prism and the number of cubes required.