# Pyramid + triangle - math problems

1. Secret treasure Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
2. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
3. Tower The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m2 of the sheet is required to cover the top of the tower if we count 8% of the sheet waste?
4. Pyramid roof 2/4 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
5. Tetrahedral pyramid Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm. How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
7. Pyramid - angle Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
8. 4side pyramid Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
9. Tetrahedral pyramid Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
10. Triangular pyramid Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
11. House roof The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
12. Pentagonal pyramid Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 7.7 cm and a plane ABV, ABC has angle 37 degrees.
13. Triangular pyramid It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
14. Hexagonal pyramid Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
15. Square pyramid Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
16. Pyramid Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
17. Triangular pyramid Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
18. Tetrahedral pyramid It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
19. Lamp cone Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.
20. Hexagonal pyramid Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.

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