A cuboid of length 4 cm, breadth 6 cm and height 8 cm is formed using unit cubes. all the faces of the cuboid are painted using different colours. now the cubes are separated and the cubes with no face painted are used to form a new cuboid. find the volume of the newly formed cuboid.
Answers
The length of the cuboid is 4cm
So there we can arrange 4 cubes of 1 cm each.
The width of the cuboid is 6 cm
So we can arrange 6 cubes of 1 cm each
Now when we paint 4 cubes in between are left unpainted.
That means
Width we subtract 2 cm (1 cm on each side)
Length we subtract 2 cm (1 cm on each side)
Height we subtract 2 cm ( 1 cm on each side)
So we are left with 2 cubes along length, 4 cubes along width & 6 cubes along height which shall be covered from cubes which shall get painted.
Hence the number of cubes left unpainted are
= 2 ×4 × 6
= 48 cubes
The volume of the cuboid formed by the cubes left unpainted shall be 48 cm³
Please see:
The blue cubes are the ones left unpainted.
On all surfaces all cubes shall be painted.
Hence only the cubes which are 1 cube away from the edge shall not be painted.
That is why we have subtracted 2 cm ( 1 cm cube from both sides of width , length & Height.
Answer:
do BODMAS FORMULA OF MATHS