Question

if a solid cube of total surface area S is cut into 64 identical cubes by what value would the total surface area increase​

Answer 1

Given : a solid cube of total surface area S is cut into 64 identical cubes  

To find : By what value would the total surface area increase?

Solution:

Let say Side of  of cube is  4a

Then Surface area of cube S = 6(4a)² = 96a²

Volume of cube = (4a)³ = 64a³

Cube cut in 64 cubes

Hence volume of one small cube = 64a³/64 = a³

Side of small cube = a

Surface area of small cube = 6a²

Surface area of 64 small cubes = 64 * 6a² =  384a²

increase in surface area = 384a² - 96a²  =  288a²

% increase in surface area = (288a²/96a²) * 100

= 300%  

by 300%  total surface area increase

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