Answer:
Explanation:
To find out how many cuboids of dimension 5 cm x 5 cm x 3 cm are needed to form a cube, we need to calculate the volume of both the cuboid and the cube.
The volume of the cuboid is:
5 cm x 5 cm x 3 cm = 75 cubic cm
To form a perfect cube, the volume of the cube should be a multiple of the volume of the cuboid. The smallest cube that can be formed using a multiple of 75 cubic cm is a cube with a volume of 75 x 8 = 600 cubic cm.
To find the dimensions of this cube, we need to find the cube root of 600 cubic cm:
cube root of 600 = 8.66 cm
So, the dimensions of the cube are 8.66 cm x 8.66 cm x 8.66 cm.
To find how many cuboids are needed to form this cube, we need to divide the volume of the cube by the volume of the cuboid:
Volume of the cube = 8.66 cm x 8.66 cm x 8.66 cm = 658.39 cubic cm
Number of cuboids required = 658.39 cubic cm ÷ 75 cubic cm = 8.78
Since we can't use a fraction of a cuboid, Anuj will need 9 such cuboids to make a perfect cube.