1. Find the area of the base of a regular square base pyramid whose lateral faces are equilateral triangles whose altitude is 8 dm.
2. What fraction of the volume of a pyramid must be cut off by a plane parallel to the base if the resulting pyramid has lateral area equal to ½ of the lateral area of the original pyramid.
3. Find the volume, lateral surface area and total surface area of a regular tetrahedron whose edge is 80 cm.
4. A regular triangular pyramid has an altitude of 9 dm and a volume of 46.8 dm. Find the length of the edges, lateral surface area, the total surface area.
5. An inverted square base pyramid has a height of 80 dm and the top base is a square whose edge is 300 cm. If the tank contains water with a height of 50 dm, what is the volume of the water? What volume is still to be occupied by water ? What is the wetted surface of the pyramidal tank ? Express all units in meter.
6. A rectangular base pyramid has base dimensions of 50 cm by 80 cm. If the height is 120 cm, determine the base area, volume, lateral surface area, and total surface area.
7. A right square base pyramid has a base edge of 25 cm and an altitude of 75 cm. Determine the area of a parallel section 12 cm from the base.
8. A regular pentagonal pyramid has an altitude of 80 cm and a slant height 100 cm. Determine the base area, lateral surface area, total surface area and the volume of the pyramid.
9. How far from the base of square pyramid of altitude 108 cm is a section parallel to the base which has an area equal to one-third of the area of the base.
10. Find the volume and the total lateral surface area of a hexagonal pyramid whose base edge is 8 cm and an altitude of 80 cm.