cube problem

[tytyros]

A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?

4%, 300%,75%,400%,5%

[krovvidy]

One 4cm*4cm*4cm cube = 4*4*4 1cm*1cm*1cm cubes

Surface Area of 4 cc cube = 6*4*4
Surface Area of 1 cc cube = 6*1*1
Total Surface Area of the 64 1cc cubes = 64*6

% increase = 100*(64*6-6*4*4)/6*4*4
i.e, 300%

[tytyros]

great krovvidy....there is a little variant to this problem

------------------------------------------------------
A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes?

1: 6

1: 5

1: 25

1: 125

1:435

---------------------------------------------------------

[tytyros]

6.5.5/ (125.(6.1.1)) = 25/125....1:5.
I only posted this question to reveal the twist

[vibhorsbi]

answer to this question is 300%
surface area of cube = 6a2
hence 6*4*4 = 96
no. of cubes now = 64
surface area 64*6 = 384 increase = 288
% increase = 300%

[vibhorsbi]

answer to tyro question is 5