Question

A rectangular prism with a square base is cut from the center of a triangular prism. Each side of the square base measures 1.7 units.

What is the volume of the shaded solid? Round to the nearest tenth of a cubic unit.

Answer 1

the answer is 45.4 u³.

Answer 2

Let
`V_s` be the volume of the solid S. We can write:

`V_(shaded) = V_(triangular) - V_(rectangular)`

Now, we just need to calculate the volume of the original prism (Vtriangular) and the volume that was removed (Vrectangular). So:

`\bullet ~V_(triangular) = S_(\triangle basis)* h\\\\ V_(triangular) = (5*5.7)/(2)*4\\\\ V_(triangular) = 57~u^3\\\\\\ \bullet ~V_(rectangular) = S_(\square basis)* h\\\\ V_(rectangular) = 1.7^2*4\\\\ V_(rectangular) = 11.56~u^3`

Then,

`V_(shaded) = V_(triangular) - V_(rectangular)\\\\ V_(shaded) = 57 - 11.56\\\\ V_(shaded) = 45.44~u^3\\\\ \boxed{V_(shaded) \approx 45.4~u^3}`

Thus, the answer is 45.4 u³.