Question

Each cube in this figure is a -millimeter cube. What is the total volume of the prism?

Answer 1

Answer:

The total volume of the prism is 378 mm³.

Step-by-step explanation:

The prism is made up of $6\times 3\times 4$ cubes that is $\textrm{volume of cube} = length\times breadth\times height$

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 $6\times3 = 18$ cube. So total volume for 18 cube will be

$\textrm{volume for 9} = 9\times 18 = 162\mm³}$

For 2 mm³

therefore, in first layer we have $6\times3 = 18$ cube. So total volume for 18 cube will be

$\textrm {volume for 2} = 2\times 18 = 16\mm³$

For 6 mm³

therefore, in first layer we have $6\times3 = 18$ cube. So total volume for 18 cube will be

$\textrm {volume for 6} = 6\times 18 = 108\mm³$

For 4 mm³

therefore, in first layer we have $6\times3 = 18$ cube. So total volume for 18 cube will be

$\textrm {volume for 4} = 4\times 18 = 72\mm³$

$\textrm {total volume for Prism} = \textrm{sum of volume for 9,2,6 and 4}\\= 162 + 36 + 108 + 72\\= 378$\ mm³

$= 378\ mm^{3}$