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If a solid cube of total surface area ‘S’ is cut into 64 identical cubes, by what value would the total surface area increase?

Posted by Gunjan Singh 5 years, 1 month ago

CBSE > Class 10 > Mathematics

1 answers

Gaurav Seth 5 years, 1 month ago

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

2Thank You

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