Question

A cubical cake is cut into several smaller cubes by dividing each edge into 7 equal parts. The cake is cut from the top along the two diagonals forming four prisms. Some of them get cut and rest remained in the cubical shape. A complete cubical (smaller) cake was given to adults and the cut off part of a smaller cake is given to a child (which is not an adult). If all the cakes were given equally each piece to a person, total how many people could get the cake?

• A. 343
• B. 448
• C. 367
• D. 456

Answer 1

The correct option is B 448


In the above layer, we can see that total 13 cubes get a cut. So, in 7 layers total $13\times 7=91$ cubes will get a cut and the remaining $(7^3-91)=252$ cubes are without any cut.
Total number of pieces which are not a cube
$=12\times 2\times 7+4\times 7=196$
(Since 84 cubes are diagonally cut into two parts and 7 cubes which are the centre are divided into 4 parts.)
Thus, total 196 children will get one-one piece and 252 adults get one-one piece
Thus total 252 + 196 = 448 people can get a piece of cake.