A clerk is packing cubes into a box each cube has edges of 6 inches the dimensions of the box are 15 inches by 30 i.ches by 18 inches find how many cubes will fit in the box ?
I don't know how to solve and explain how i found my answer please
The dimensions are divisible by 6 except 15 so the cubes will fit exactly on the bottom
area of 30*18 = 6*6 *15
so 15 cubes covers 30*18
now it can only be 2 cubes high because of the 15 inch height limitation
so
15*2 = 30 cubes
To solve this problem, first, we need to find the volume of one cube and the volume of the box.
The volume of one cube can be calculated by multiplying the length, width, and height of the cube. Since all edges of the cube are 6 inches long, the volume of one cube is given by:
Volume of one cube = 6 inches x 6 inches x 6 inches = 216 cubic inches
Next, we need to find the volume of the box. The volume of a rectangular box can be calculated by multiplying the length, width, and height of the box. In this case, the dimensions of the box are given as 15 inches, 30 inches, and 18 inches respectively. So, the volume of the box is:
Volume of the box = 15 inches x 30 inches x 18 inches = 8,100 cubic inches
To find the number of cubes that can fit in the box, we need to divide the volume of the box by the volume of one cube:
Number of cubes that can fit = Volume of the box / Volume of one cube
Number of cubes that can fit = 8,100 cubic inches / 216 cubic inches
Number of cubes that can fit = 37.5 cubes (approximately)
Since we cannot have a partial cube, we round down to the nearest whole number. Therefore, you can fit 37 cubes in the box.
To find out how many cubes can fit into the box, you need to determine the volume of both the cube and the box, and then divide the volume of the box by the volume of the cube.
The volume of a cube is calculated by cubing the length of one side. In this case, since each side of the cube has an edge of 6 inches, the volume of the cube is 6^3 = 216 cubic inches.
Now, calculate the volume of the box by multiplying its length, width, and height. In this case, the box has dimensions of 15 inches by 30 inches by 18 inches, so the volume of the box is 15 x 30 x 18 = 8100 cubic inches.
Lastly, divide the volume of the box by the volume of the cube to find the number of cubes that can fit in the box: 8100 cubic inches / 216 cubic inches = 37.5.
Since it is not possible to have a fractional number of cubes, you can conclude that a maximum of 37 cubes can fit in the box.