Quantitive Aptitude

Question

Susan made a block with small cubes of volume 8 cubic cm to make a block, 3 small cubes long , 9 small cubes wide and 5 small cube deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to lock like a block with same dimension , if it were made hollow. What is the minimum number of cubes that she needs to make the block?

a)114

b) 135

c) 31

d)71

Comments

is it 31 ?
(i don't know i have properly understood the question or not)
edit : this is wrong ans

Answer 1

114 A is the correct answer

Answer 2

We have got a 3 x 9 x 5 cube. The dimension does not really matter.

Cut the cube into three layers – top, middle and bottom.

To get a hollow cube, we need the top and the bottom layer. From the middle layer, when we remove the core which is the unpainted cubes, we get the material for the hollow cube.

Initially we have 3 x 9 x 5 cubes = 135 small cubes . This forms the solid cube.

The top layer has 1 x 9 x 5 cubes = 45 cubes which are needed for the hollow cube. And like this we need the 45 cubes from the bottom also. \

In the middle layer, we have 45 cubes. But we do not need the core of the cube of dimension 1 x 7 x 3 = 21 cubes. We remove this from 45 to get 24 cubes.

Hence the total no. of cubes needed to make a hollow cube is =

45 + 45 + 24 = 114 cubes