Question

Find the volume of composite figure, first find thee volume of the rectangular prism

Answer 1

We need to find the volume of the composite figure.

The volume of a rectangular pyramid having a base with dimensions a and b, and an altitude h is:

`\frac{}{}(a\cdot b\cdot h)/(3)`

In this problem, we have:

`\begin{gathered} a=12ft \\ b=10ft \\ h=3ft \end{gathered}`

Thus, the volume of the rectangular pyramid is:

`(12ft\cdot10ft\cdot3ft)/(3)=12\cdot10\cdot(3)/(3)ft\cdot ft\cdot ft=120ft^3`

Now, the volume of a rectangular prism with dimensions a, b, and c, is given by:

`a\cdot b\cdot c`

The lengths a and b are the same as above, and c = 7ft.

Thus, the volume of the prism is:

`12ft\cdot10ft\cdot7ft=12\cdot10\cdot7ft\cdot ft\cdot ft=840ft^3`

Therefore, the volume of the composite figure is:

`120ft^3+840ft^3=960ft^3`

Answer:

• Rectangular Pyramid Volume =, 120 ,ft³

• Rectangular Prism Volum = ,840, ft³

• Total Volume of Composite Figure = ,960, ft³