Area and volume

Exercise 1

Compute the area of the following solids.

Exercise 2

Here you see a so called hipped roof, a roof with a rectangular base $A B C D$ with the roof-ridge $E F$ situated exactly over the middle of the base. The roof itself consists of twee equilateral triangles and two symmetric trapeziums.

Compute the area of this hipped roof.

Exercise 3

The base of a pyramid $T . A B C D E$ is a regular pentagon $A B C D E$ . The height of the pyramid is $T S$ , where point $S$ is the center of the circle through the corner points of the base. All edges of the pyramid are $4$ cm.

Compute the area of this pyramid.

Exercise 4

Below you see a side view of a circular tent.

Compute the amount of tent fabric, i.e. the area, you would need to make this tent.

Exercise 5

Arab whirling dervishes often wear a so called cone skirt. This is a skirt that widens from the waist down. If the fabric would be stiff it would look like a cone without the pointed top. Here you see the template for such a skirt.

Compute how much cloth you would need to make such a skirt in cm².

Exercise 6

The figure to the right is a regular octagonal antiprism. Such figures and their templates can be found on de website korthalsaltes.com.
All edges of this antiprism are $5$ cm.

Compute the area of this antiprism.

Exercise 7

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 in Tegelen. 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 $1$ of $2$ persons.

What area 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 area for a sphere segment with a height of $h$ for a sphere with radius $r$ . The area of such a segment is $2 π r h$ .

Exercises