Question

side of a cube is 1cm.If by fixing such 64 cubes a new cube is made then find the total surface area of new cube.

Answer 1

Number of cubes is calculated in terms of volume of original bigger cube and the volume of newer smaller cubes formed out of the original cube.


the volume original bigger cube of edge of 4 cm is = 4*4*4 = 64 cubic cm.


the volume of smaller cube of edge 1 cm is = 1*1*1 = 1 cubic cm.


number of smaller cubes formed out of original cube is = vol of bigger cube/vol of smaller cube = 64/1 =64 cubes formed out of original cube.


the surface area of cube is = 6*edge*edge sq cm


surface area of bigger cube is = 6*4*4 = 96 sq cm


surface area of all smaller cubes is = 64*6*1*1 = 384 sq cm


percentage change therfore is =( change/original ) *100


= (288/96)*100 = 300% change in the new surface area (Ans)