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

Step-by-step explanation:

let the side of cube be a

then,

6a^2=S-----------------(1)

volume=a^3-----------(2)

let the side of small cube be x

then,

64*6x^2=S'-----------(3)

volume=64*x^3--------(4)

from eq. 2 and 4,

a^3=64*x^3--------(5)

=> a^3/x^3=64------(6)

on multiplying x and divide x in eq. 3,

(64*x^3)6/x=S'

from equ. (5),

(a^3*6)/x=S'

now,from equ 1. (6a^2=S)

S*a/x=S'

On cubing both side,

S^3(a/x)^3=S'^3

now from equ. 6,

S^3*64=S'^3

=> S'=4S

so new surface area is four time the bigger cube

Answer 2

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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