Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the dimension of each prism is not given.
So, I will give a general explanation.
From the question, we understand each prism.
So, to get the new volume; we simply add up the volume of each prism.
For instance (we want to make assumptions)
Rachel
[tex]Length = 4; Width = 3; Height = 4[/tex]
Timothy
[tex]Length = 6; Width = 3; Height = 4[/tex]
Robyn
[tex]Length = 4; Width = 8; Height = 3[/tex]
So, we have:
[tex]Volume = Length * Width * Height[/tex]
For each, we have:
[tex]Rachel =4* 3* 4 =48[/tex]
[tex]Timothy= 6* 3* 4 = 72[/tex]
[tex]Robyn = 4* 8* 3 = 96[/tex]
The volume of the new
[tex]Volume = 48 + 72 + 96[/tex]
[tex]Volume = 216[/tex]
The dimension of new prism.
Using the assumed values, we have:
[tex]Length = 4; Width = 3; Height = 4[/tex]
[tex]Length = 6; Width = 3; Height = 4[/tex]
[tex]Length = 4; Width = 8; Height = 3[/tex]
Now, we consider the measure of the sides
Sides with the same length will form a new side.
Side 1
[tex]Length =4[/tex] --- Rachel
[tex]Height = 4[/tex] ---- Timothy
[tex]Length = 4[/tex] --- Robyn
The above lengths have the same measure. So, one of the sides of the new prism will assume the value of this length.
So:
[tex]Length = 4[/tex] -- for the new prism
Side 2
[tex]Width =3[/tex]
[tex]Width = 3[/tex]
[tex]Height = 3[/tex]
The above lengths have the same measure. So, one of the sides of the new prism will assume the value of this length.
So:
[tex]Width = 3[/tex] -- for the new prism
Side 2
[tex]Height = 4[/tex]
[tex]Length = 6[/tex]
[tex]Width =8[/tex]
For this, we simply add up each length.
So, we have:
[tex]Height = 4 + 6 + 8[/tex]
[tex]Height = 18[/tex] --- for the new prism
So, the new dimension is:
[tex]Length = 4[/tex]
[tex]Length = 6[/tex]
[tex]Height = 18[/tex]
[tex]Volume = 4 * 3 * 18[/tex]
[tex]Volume = 216[/tex]
