# Pyramid + diagonal - practice problems

#### Number of problems found: 15

- Billiard balls

A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. - Quadrilateral pyramid

In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place. - Hexagon rotation

A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated? - 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. - Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.) S =? , V =? - Tetrahedral pyramid

Calculate the regular tetrahedral pyramid's volume and surface if the content area of the base is 20 cm^{2}, and the deviation angle of the side edges from the plane of the base is 60 degrees. - Distance of points

A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - 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 - Quadrilateral pyramid

In a regular quadrilateral pyramid, the side edge is e = 7 dm, and the diagonal of the base is 50 cm. Calculate the pyramid shell area. - Square pyramid

Calculate the pyramid's volume with the side 5 cm long and with a square base, and the side-base has an angle of 60 degrees. - 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. - The pyramid 4s

The pyramid with a rectangular base measuring 6 dm and 8 dm has a side edge of length 13 dm. Calculate the surface area and volume of this pyramid. - Tetrahedral pyramid

It is given a regular tetrahedral pyramid with a base edge of 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges. - Height of pyramid

The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height? - Right pyramid

A right pyramid on a base 4 cm square has a slanted edge of 6 cm. Calculate the volume of the pyramid.

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Pyramid practice problems. Diagonal - practice problems.