64 small but identical cubes have been put together to form a large cube. How many more such small cubes will have to remove to make this large cube hollow.
Answers
8 small cubes need to be removed to make large cube hollow if 64 small identical cubes have been put together to form a large cube.
Given:
64 small identical cubes have been put together to form a large cube.
To Find:
How many small cubes need to be removed to make this large cube hollow.
Solution:
Volume of a cube = (side)³
Step 1 :
Assume side of Small Cube = a unit
Step 2 :
Find volume of small cube
= a³
Step 3 :
Find volume of Large cube multiplying by 64
= 64a³
= (4a)³
Step4 :
Find Side length of large cube
= 4a units
Step 5:
To make hollow cube (4a - 2a)³ need to be removed
= (2a)³
= 8a³
= 8 small cubes
Hence, 8 small cubes need to be removed to make large cube hollow.
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