# Diagonal + pyramid - math problems

#### Number of problems found: 12

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.
• 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 slant edge of 6 cm. Calculate the volume of the pyramid.
• 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.
• Square pyramid
Calculate the pyramid's volume with the side 5cm long and with a square base, side-base has an angle of 60 degrees.
• Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the content area of the base is 20 cm2, and the deviation angle of the side edges from the plane of the base is 60 degrees.
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
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 =?
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.
• 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.
• 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?
• 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.

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Diagonal - math word problems. Pyramid Problems.