Question

What is the volume of the given cube (in cm3), if the black portion represents holes made from one end of the cube to the other? (Assume that the cube is made of smaller cubes of volume 1 cm3)
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Answer 1

Step-by-step explanation:

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1. thanks my answer... ..

Answer 2

Answer:

The volume of the cube is $88 cm^{3}$.

Step-by-step explanation:

Step 1:

Each side of the bigger cube is made up of 25 smaller cubes.

So, the bigger cube is altogether made up of 25×5=125 smaller cubes.

The small cubes have a volume of $1cm^{3}$.

Therefore, the actual volume of the bigger cube is $125cm^{3}$.

Step 2:

The black portion represents holes that are made from one end to the other end.

Taking the front side, 3 cubes are removed from the center column.  

So, a total of 15 cubes are removed.

Step 3:

Taking the upper side, 3 cubes are removed from the center row.

So, a total of 15 cubes are removed. But 3 cubes are common with the cubes removed from the front side. Therefore, subtracting them, only 12 cubes are removed.

Step 4:

Taking the right side, 3 cubes are removed from the center row.

So, a total of 15 cubes are removed. But 5 cubes are common with the cubes removed from the front and upper side. Therefore, subtracting them, only 10 cubes are removed.

Hence, a total of 37 cubes are removed.

The volume of the holes is then $37cm^{3}$.

Step 5:

Volume of given cube = Actual volume - Volume of the holes

Volume of given cube = 125 - 37

Volume of given cube = $88cm^{3}$

Therefore, the volume of the required cube is $88cm^{3}$.

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