Question

A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is. 

(A) 56 

(B) 64 

(C) 72 

(D) 96

Answer 1

Correct option is (D) 96

Four blocks are needed for each direction(totally 3 directions) to build a bigger cube containing 64 blocks. So area of one side of the bigger cube = 4 x 4 = 16units

There are 6 faces so total area = 6 x16 = 96units 

When cubes at the corners are removed they introduce new surfaces equal to exposes surfaces so the area of the bigger cube does not change from 96