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Mathematics-Online problems: | ||

## Solution to the problem of the (previous) week |

** Problem:**

Find the points of intersection
on the edges.

Compute the volumes of the tetrahedron and of the solid subfigure containing the origin .

*Hint:*
The dashed triangle
dissects one of the solid subfigures into a prism and a pyramid having a quadrilateral base.

**Answer:**

( , , ) | |||

( , , ) | |||

( , , ) | |||

( , , ) | |||

(The results should be correct to three decimal places.)

** Solution:**

i. e.

i. e.

i. e. and

i. e. and

The area of the base triangle of the tetrahedron is

Hence, for the volume of the tetrahedron we get

The prism with base and height has the volume

The base of the pyramid is a trapezoid with vertices
.

Its area is

Hence, the solid subfigure containing the origin has the volume

[problem of the week]