A metallic rectangular cuboid of dimensions 4cm X 6cm X 8cm is melted

1.	A metallic rectangular cuboid of dimensions 4cm X 6cm X 8cm is melted and some more metal is added to make it a cube, the measure of whose side is an integer. What is the minimum volume of metal to be added and what is the side of the cube?Please give the solution not the method..
Answer» Dimensions of CUBOID are 4cm X 6cm X 8cm. Volume of a cuboid = Length $\times$ Width $\times$ Height So, volume of given cuboid = 4 $\times$ 6 $\times$ 8 = 192 $cm^3$ It is given that the cuboid is converted to a CUBE. Volume of cube = $(Side)^{3}$ It is given that some MINIMUM volume is added to cuboid to MAKE cube whose side is an integer. If we have a look at the perfect cube integers, cube nearest to 192 is 216. So, Minimum volume of metal to be added = 216 - 192 = 24 $cm^3$ Also, Volume of cube = $(Side)^{3}$ 216 = $(Side)^{3}$ $\Rightarrow \text{Side = 6 cm}$ So, minimum volume of metal to be added is 24 $cm^3$ and side of cube is 6 cm.

A metallic rectangular cuboid of dimensions 4cm X 6cm X 8cm is melted and some more metal is added to make it a cube, the measure of whose side is an integer. What is the minimum volume of metal to be added and what is the side of the cube?Please give the solution not the method..

Answer»

Dimensions of CUBOID are 4cm X 6cm X 8cm.

Volume of a cuboid = Length $\times$ Width $\times$ Height

So, volume of given cuboid = 4 $\times$ 6 $\times$ 8 = 192 $cm^3$

It is given that the cuboid is converted to a CUBE.

Volume of cube = $(Side)^{3}$

It is given that some MINIMUM volume is added to cuboid to MAKE cube whose side is an integer.

If we have a look at the perfect cube integers, cube nearest to 192 is 216.

So, Minimum volume of metal to be added = 216 - 192 = 24 $cm^3$

Also, Volume of cube = $(Side)^{3}$

216 = $(Side)^{3}$

$\Rightarrow \text{Side = 6 cm}$

So, minimum volume of metal to be added is 24 $cm^3$ and side of cube is 6 cm.