Question:
1. The edge lengths of a right rectangular prism are
1/2 meter, 1/2 meter, and 3/4 meter. How many unit cubes with edge lengths of 1/12 meter can fit inside?
Someone please help me. I dont understand this at all, so I can't give you my answer. If anyone could simplify the question or give me the answer so I can put it into my own words, that would be great. Thanks
you can do it in a few ways. One way is to see how many small cubes fit in each dimension
1/2 = 6/12
3/4 = 9/12
so, the block can hold 6*6*9 = 324 small cubes
Or, 1/2 * 1/2 * 3/4 = 3/16 m^3
scale that by a factor of 12 and the volume scales by a factor of 12^3
3/16 * 12^3 = 324
trash
Thanks mate :)
Vp = L*W*h = 1/2 * 1/2 * 3/4 = 3/16 m^3 = Vol. of prism.
Vc = L*W*h = 1/12 * 1/12 * 1/12 = 1/1728 m^3 = Vol. of cube.
Vp/Vc = (3/16)/(1/1728) = 3/16 * 1728/1 = 324 Cubes.
To solve this problem, we need to find the volume of the right rectangular prism and then determine how many unit cubes with edge lengths of 1/12 meter can fit inside.
1. The volume of a rectangular prism is calculated by multiplying the lengths of its three edges. In this case, the lengths are 1/2 meter, 1/2 meter, and 3/4 meter. To find the volume, we multiply all three lengths together:
Volume of the rectangular prism = (1/2) * (1/2) * (3/4)
2. To simplify the calculation, we can multiply the fractions first:
Volume = (1/4) * (3/4) = 3/16
3. The result of the multiplication is 3/16. This means the rectangular prism has a volume of 3/16 cubic meters.
4. Now, we need to determine how many unit cubes with edge lengths of 1/12 meter can fit inside this rectangular prism. To do this, we divide the volume of the rectangular prism by the volume of a unit cube.
5. The volume of a unit cube with edge length 1/12 meter is calculated by multiplying all three edges, which are all 1/12 meter:
Volume of a unit cube = (1/12) * (1/12) * (1/12) = 1/1728
6. To find how many unit cubes can fit inside the rectangular prism, we divide the volume of the rectangular prism by the volume of the unit cube:
Number of unit cubes = (3/16) / (1/1728)
7. To divide fractions, we multiply the numerator by the reciprocal of the denominator:
Number of unit cubes = (3/16) * (1728/1)
8. Simplifying the multiplication:
Number of unit cubes = (3 * 1728) / 16
9. Finally, we calculate the multiplication:
Number of unit cubes = 5184 / 16 = 324
Therefore, the answer is that 324 unit cubes with edge lengths of 1/12 meter can fit inside the given right rectangular prism.