A 4" × 6" × 8" rectangular solid is cut by slicing through the midpoints of three adjacent sides as shown. Find the volume of the outlined solid.

Guest Feb 27, 2021

#1**0 **

We can use 3d vectors. This pyramid is spanned by the vectors (2,0,0), (0,3,0), and (0,0,4). Taking the determinant gives us a volume of 8.

Guest Feb 27, 2021

#3**0 **

The area of the triangular pyramid is $\frac{1}{3} bh. $ We can make the base the top face, and the base has an area of $\frac{3 \cdot 4}{2} = 6.$ The height that is given is $\frac{1}{2} \cdot 4 = 2.$ Now, we can plug these values in, and we get $$V = \frac{1}{3} bh. $$ $$V = \frac{1}{3} (6)(2)$$ $$\boxed{V = 4 \text{ in}^3}.$$

BigBurger Feb 27, 2021