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?

A 3S
B 6S
C 8S
D 63S​

Answer 1

Answer:

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)? = 96a? = Volume of cube = (4a) = 64a3

Cube cut in 64 cubes

Hence volume of one small cube = 64a /64 = a 3 a

Side of small cube = a

Surface area of small cube 6a? Surface area of 64 small cubes = 64 * 6a? = 384a?

increase in surface area = 384a? - 96a?

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

= 300%

by 300% total surface area increase