How many cubes with 1/4-foot side lengths will fit inside 77ft3 if they are packed with no gaps
4 small cubes will fit into a 1-ft length.
So, 4^3 = 64 small cubes will fit into each cubic foot.
64*77 small cubes fit into 77 ft^3.
Assuming the dimensions of the large solid are multiples of 3 inches ...
To find out how many cubes with 1/4-foot side lengths will fit inside 77ft³ without any gaps, we need to calculate the volume of each cube and then divide the total volume of the given space by the volume of each cube.
The volume of a cube is determined by multiplying the length, width, and height. In this case, the side length is given as 1/4 foot, so the volume of each cube can be calculated as:
Volume of each cube = (1/4 ft)³ = 1/4 ft * 1/4 ft * 1/4 ft = 1/64 ft³
Now, to determine the number of cubes that can fit inside 77ft³, we divide the total volume of the given space by the volume of each cube:
Number of cubes = 77 ft³ / (1/64 ft³)
To simplify this division, we can invert and multiply:
Number of cubes = 77 ft³ * 64 ft³ / 1 ft³
Number of cubes = 4928 ft³ / 1 ft³
Finally, we can simplify the expression:
Number of cubes = 4928
Therefore, 4928 cubes with 1/4-foot side lengths will fit inside 77ft³ if they are packed without any gaps.
To find out how many cubes with 1/4-foot side lengths will fit inside 77ft³ without any gaps, we need to calculate the volume of each cube and then divide the total volume of the space (77ft³) by the volume of one cube.
Step 1: Calculate the volume of one cube
The volume of a cube is found by multiplying the length, width, and height of the cube. Since the side lengths are given as 1/4 foot, we need to convert this to feet: 1/4 foot = 0.25 feet.
Volume of one cube = (0.25 ft) × (0.25 ft) × (0.25 ft) = 0.015625 ft³
Step 2: Calculate the number of cubes that can fit
Now, we divide the total volume of the space (77 ft³) by the volume of one cube (0.015625 ft³) to calculate the number of cubes that can fit without any gaps:
Number of cubes = 77 ft³ / 0.015625 ft³ ≈ 4928
Therefore, approximately 4928 cubes with 1/4-foot side lengths can fit inside 77ft³ when packed without any gaps.