Here you see a so called hipped roof, a roof with a rectangular base $ABCD$ with the roof-ridge $EF$ situated exactly over the middle of the base. The roof itself consists of twee equilateral triangles and two symmetric trapeziums. Compute the volume under this hipped roof.

A pyramid $T.ABCDE$ has as its base a regular pentagon $ABCDE$ . The height of the pyramid is $TS$ , where point $S$ is the centre of the circle that bounds the corners of the base. All edges of this pyramid are $4$ cm long.
Compute the volume of this pyramid. 

Here you see a side view of a circular tent.
Compute the volume of this tent.

Given is an L-shaped cylindrical hollow steel pipe. The square ground plate of $150$ mm by $150$ mm is connected to the wall, the pipe then sticks out by $450$ mm forward and upwards by $250$ mm. The inner diameter of the pipe is $48$ mm and the steel is $1$ mm thick.
Steel weighs $\mathrm{7,8}$ g/cm³.
What is the combined weight of the pipe and the ground plate?

The fifty well known sphere houses with their striking architecture are located in ’s-Hertogenbosch. The sphere house was designed by the sculptor, designer and architect Dries Kreijkamp born in 1937 inTegelen. They were build in 1984 in order to connect the inhabitants with nature by means of the several round windows present in the houses. The houses are also environmentally friendly, because of the spherical shape the wind can hardly get a grip and they were designed to be energy efficient and cheap. The houses can be rented for $1$ or $2$ persons.
What volume do these sphere houses have if the diameter of the sphere itself is $8$ meters and that of the cylinder is $6$ meters, while the height of the cylinder is $3$ meters? use the formula for the volume of a sphere segment with height $h$ for a sphere with radius $r$ . The volume of such a segment is $\frac{1}{3}\pi h^2(3R-h)$ .