Pyramid Problems
Number of problems found: 128
- School model
The beech school model of a regular quadrilateral pyramid has a base 20 cm long and 24 cm high. Calculate a) the surface of the pyramid in square decimeters, b) the mass of the pyramid in kilograms if the density of the beech is ρ = 0,8 g/cm ^ 3 - How to
How to find a total surface of a rectangular pyramid if each face is to be 8 dm high and the base is 10 dm by 6 dm. - Tower
Charles built a tower of cubes with an edge 2 cm long. In the lowest layer there were 6 cubes (in one row) in six rows, in each subsequent layer always 1 cube and one row less. What volume in cm3 did the whole tower have? - Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm2 greater than the upper base's content. Calculate the area of the upper base. - The roof
The roof of the tower has the shape of a regular quadrangular pyramid, the base edge of which is 11 m long and the side wall of the animal with the base an angle of 57°. Calculate how much roofing we need to cover the entire roof, if we count on 15% waste - Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid. - Pyramid of Giza
The Great Pyramid of Giza has the shape of a regular quadrangular pyramid. The base edge is 227 m long and 140 m high. What is the weight of the stone needed to build this pyramid, if the weight of 1 m3 of stone is 2.5 t? - Truncated pyramid
Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm. - Truncated pyramid
Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm and the angle that the side wall with the base is 42 degrees - Pentagonal pyramid
The height of a regular pentagonal pyramid is as long as the edge of the base, 20 cm. Calculate the volume and surface area of the pyramid. - Regular 4-sided pyramid
Find the area (surface area) of a regular 4-sided pyramid if its height is 20 m and the wall height is 23 m. - Special body
Above each wall of a cube with an edge a = 30 cm, a regular quadrilateral pyramid with a height of 15 cm is constructed. Find the volume of the resulting body. - Quadrilateral pyramid
Find the height and surface of a regular quadrilateral pyramid with a base edge a = 8cm and a wall height w = 10cm. Sketch a picture. - Triangular pyramid
Calculate the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height v = 20cm. - The pyramid
The pyramid with a square base is 50 m high and the height of the sidewall is 80 m. Find the endge of the base of the pyramid. - Pentagonal pyramid
Find the volume and surface of a regular pentagonal pyramid with a base edge a = 12.8 cm and a height v = 32.1 cm. - Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base - From plasticine
Michael modeled from plasticine a 15 cm high pyramid with a rectangular base with the sides of the base a = 12 cm and b = 8 cm. From this pyramid, Janka modeled a rotating cone with a base diameter d = 10 cm. How tall was Janka's cone? - Find the
Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm3 and a height of 45 cm.
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