+0  
 
0
29
3
avatar

Find the volume of a rectangular solid if the areas of three of its adjacent faces are 12, 8, 6

 

Please explain ur answer too

 Jul 3, 2023
 #1
avatar+676 
0

 

Find the volume of a rectangular solid if the areas of three of its adjacent faces are 12, 8, 6  

 

If the dimensions are 4 x 3 x 2 you get those areas.   

I can't figure out another way to get the same areas.  

 

So the volume would be 4 x 3 x 2  =  24 cubic units   

.

 Jul 3, 2023
 #2
avatar+676 
0

 

I don't know if it's a coincidence,   

but if you mutiply those areas                        12 x 8 x 6 = 576   

 

then take the sqrt of the product                    sqrt(576) = 24    

 

that's the same as the volume.  

.

Bosco  Jul 4, 2023
 #3
avatar+676 
0

 

Oh, I see how it works now   

 

                                                      area1  x  area2  x  area3     

 

                                                     (4 x 3)  x  (4 x 2)  x  (3 x 2)    

remove parentheses                      4 x 3   x   4 x 2   x   3 x 2      

rearrange and group                     (4 x 3 x 2)   x   (4 x 3 x 2)  

 

                                                                   24  x  24    

That's how it happens  

.

Bosco  Jul 4, 2023

3 Online Users

avatar