A Box 4 Cm By 10 Cm Is To Be Filled Up With Cubes.If A Cube Measures 1 Cm On Each Edge,How Manyvcubes Can Fit Exactly Inside The Box?

A box 4 cm by 10 cm is to be filled up with cubes.if a cube measures 1 cm on each edge,how manyvcubes can fit exactly inside the box?

 

Answer:

  1. If the height of the box is 4 cm (4 cm by 10 cm by 4 cm), then 160 cubes can fit inside the box.
  2. If the height of the box is 10 cm (4 cm by 10 cm by 10 cm), then 400 cubes can fit inside the box.

Step-by-step explanation:

Step 1: Write the given

  1. A box 4 cm by 10 cm
  2. A cube measuring 1 cm on each edge

Step 2: Identify the volume of the cube

  1. The volume of a cube is (side)(side)(side) or side^{3} (since the height, length, and width which are considered as the sides are equal)
  2. As side=1 cm, then the volume of the cube is equivalent to 1 cm^{3}; thus, there is 1 cubic cm per cube

Step 3: Identify the volume of the box

Since the height, length, and width is not clearly specified, then I would just assume that the box is either 4 cm by 10 cm by 4 cm or 4 cm by 10 cm by 10 cm in measurement.

  1. Volume of box=(length)(height)(width)
  2. For 4 cm by 10 cm by 4 cm box, the volume is equal to 160 cubic cm.
  3. For 4 cm by 10 cm by 10 cm box, the volume is equal to 400 cubic cm.

Step 4: Determine the number of cubes that can fit inside the box

For 4 cm by 10 cm by 4 cm box,

160 cm^{3} *\frac{cube}{1 cm^{3} }= 160 cubes

Therefore, 160 cubes can fit exactly inside the box of 4 cm by 10 cm by 4 cm.

For 4 cm by 10 cm by 10 cm box,

400 cm^{3} *\frac{cube}{1 cm^{3} }= 400 cubes

Therefore, 400 cubes can fit exactly inside the box of 4 cm by 10 cm by 10 cm.


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