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

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:

$\bullet ~V_{triangular} = S_{\triangle basis}\times h\\\\ V_{triangular} = \dfrac{5\times5.7}{2}\times4\\\\ V_{triangular} = 57~u^3\\\\\\ \bullet ~V_{rectangular} = S_{\square basis}\times h\\\\ V_{rectangular} = 1.7^2\times4\\\\ V_{rectangular} = 11.56~u^3$

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.

Answer 2

Answer:

the answer is 45.4 u³.