Answer:
Prism Y
[tex]Height = 12in[/tex]
[tex]Length = 6in[/tex]
[tex]Width = 4in[/tex]
[tex]Volume = 288in^3[/tex]
Prism Z
[tex]Height = 18in[/tex]
[tex]Length =10in[/tex]
[tex]Width = 10in[/tex]
[tex]Volume = 1800in^3[/tex]
[tex]Total = 2088in^3[/tex]
Step-by-step explanation:
Given
See attachment for sculpture
Solving (a) The dimension and volume of Y
From the attachment
[tex]Height = 18 - 6[/tex]
18 in is the height of Z and 6in represents the length (height) of the unoccupied space by Y
So:
[tex]Height = 12in[/tex]
[tex]Length = 16 - 10[/tex]
16 in is the total length of the sculpture and 10 in represents the length of Z
So:
[tex]Length = 6in[/tex]
[tex]Width = 10 - 6[/tex]
10 in is the width of Z and 6in represents the length (width) of the unoccupied space by Y
So:
[tex]Width = 4in[/tex]
Hence, the dimension of Y is:
[tex]Height = 12in[/tex]
[tex]Length = 6in[/tex]
[tex]Width = 4in[/tex]
Volume is then calculated as:
[tex]Volume = Length * Width * Height[/tex]
[tex]Volume = 12in * 6in * 4in[/tex]
[tex]Volume = 288in^3[/tex]
Solving (b) The dimension and volume of Z
As identified in (a), the dimensions of Z are:
[tex]Height = 18in[/tex]
[tex]Length =10in[/tex]
[tex]Width = 10in[/tex]
Volume is then calculated as:
[tex]Volume = Length * Width * Height[/tex]
[tex]Volume = 18in * 10in * 10in[/tex]
[tex]Volume = 1800in^3[/tex]
Solving (c): Total volume of the sculpture.
To do this, we simply add up the volumes of Y and Z.
So, we have:
[tex]Total = 288in^3 + 1800in^3[/tex]
[tex]Total = 2088in^3[/tex]
