Question

Find the volume of the composite solid.

A. 420 ft^3
B. 530 ft^3
C. 630 ft^3
D. 840 ft^3

Answer 1

THe bottom rectangular prism has volume 8*7.5*7 = 420 cu ft

The top triangular prism has a volume of 1/2 * 7 * 7.5 * 8 = 210 cu ft

Total volume = 420+210 = 630 cu ft

Answer 2

`V=630ft^3`

Explanation:

This solid is composite by a triangular prism and a rectangular prism. So, let:

`V_1=Volume\hspace{3}of\hspace{3}the\hspace{3}rectangular\hspace{3}prism\\V_2=Volume\hspace{3}of\hspace{3}the\hspace{3}triangular\hspace{3}prism`

Hence, the volume of the composite solid is:

`V=V_1+V_2`

The volume of the rectangular prism is given by:

`V_1=l*w*h`

Where:

`l=length=8ft\\w=width=7.5ft\\h=height=7ft`

So:

`V_1=8*7.5*7=420ft^3`

The volume of the triangular prism is given by:

`V_2=(1)/(2) l*b*h`

Where:

`l=Distance\hspace{3} between\hspace{3} the\hspace{3} triangular \hspace{3}faces=8ft\\b=length\hspace{3}of\hspace{3} one\hspace{3} side \hspace{3}of\hspace{3} the \hspace{3}triangle=7.5ft\\h=length \hspace{3} of \hspace{3} an \hspace{3}altitude \hspace{3} drawn \hspace{3} to \hspace{3} that \hspace{3}side=7ft`

So:

`V_2=(8*7.5*7)/(2) =210ft^3`

Therefore:

`V=420ft^3+210ft^3=630ft^3`