Answer:
The total volume of the prism is 378 mm³.
Step-by-step explanation:
The prism is made up of [tex]6\times 3\times 4[/tex] cubes that is [tex]\textrm{volume of cube} = length\times breadth\times height[/tex]
In this figure,the prism is made up of four different cube that is of volume as 9 mm³, 2 mm³, 6 mm³ and 4 mm³.
Therefore, it is only possible to have four different cube in height only.
So we will calculate the volume layer by layer.
First for 9 mm³
therefore, in first layer we have [tex]6\times3 = 18[/tex] cube. So total volume for 18 cube will be
[tex]\textrm{volume for 9} = 9\times 18 = 162\mm³}[/tex]
For 2 mm³
therefore, in first layer we have [tex]6\times3 = 18[/tex] cube. So total volume for 18 cube will be
[tex]\textrm {volume for 2} = 2\times 18 = 16\mm³[/tex]
For 6 mm³
therefore, in first layer we have [tex]6\times3 = 18[/tex] cube. So total volume for 18 cube will be
[tex]\textrm {volume for 6} = 6\times 18 = 108\mm³[/tex]
For 4 mm³
therefore, in first layer we have [tex]6\times3 = 18[/tex] cube. So total volume for 18 cube will be
[tex]\textrm {volume for 4} = 4\times 18 = 72\mm³[/tex]
[tex]\textrm {total volume for Prism} = \textrm{sum of volume for 9,2,6 and 4}\\= 162 + 36 + 108 + 72\\= 378[/tex]\ mm³
[tex]= 378\ mm^{3}[/tex]
