A hollow cube of internal edge is 22cm is filled with spherical marbles of diameter 0.5cm and it is assumed that 1/8 space of the cube remain unfilled.Then the number of marbles that the cube can accomodate is?
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To find the number of marbles that the cube can accommodate, we need to calculate the volume of the cube and the volume of each marble. Then we can divide the volume of the cube by the volume of each marble to get the total number of marbles.
1. Calculate the volume of the cube:
The internal edge of the cube is given as 22cm. Since it is a hollow cube, the volume can be calculated as the difference between the volume of the outer cube and the volume of the inner cube.
- Volume of outer cube = (22 cm)^3
- Volume of inner cube = (22 cm - 2 * 0.5 cm)^3
- Calculate the difference between these two volumes to get the volume of the hollow cube.
2. Calculate the volume of each marble:
The diameter of each marble is given as 0.5 cm, which means the radius is 0.25 cm. The volume of each sphere can be calculated using the formula: V = (4/3) * π * r^3, where V is the volume of the sphere and r is the radius of the sphere.
3. Divide the volume of the cube by the volume of each marble:
Now, divide the volume of the cube by the volume of each marble to get the total number of marbles that can be accommodated in the cube. Keep in mind that 1/8 of the cube remains unfilled, so multiply the calculated number by 7/8.
Following these steps will provide you with the answer to the question.