# Solid geometry, stereometry - page 90 of 92

Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry involves the measurements of volumes of various solid figures (three-dimensional figures), including pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones; and balls bounded by spheres.

#### Number of problems found: 1830

- Quadrilateral 5112

The body diagonal of a regular quadrilateral prism forms an angle of 60 ° with the base. The edge of the base is 20 cm long. Calculate the volume of the body. - Calculate 3019

The height is 5 cm, and the size of the angle that the side of the cone with the base makes is 63 degrees. Calculate the surface and volume of this cone. - Angle of two lines

There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - 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. - Quadrilateral prism

The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism. - 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 - Diagonal

Determine the dimensions of the cuboid, if diagonal long 60 dm has an angle with one edge 35° and with another edge 77°. - Horizontal 6161

We have a horizontal tank in the shape of a rainwater cylinder, 3.45 m long and 1.7 m wide. (only up to a height of 85 cm) - Cone

Calculate volume and surface area of the cone with a diameter of the base d=15 cm and side of the cone with the base has angle 52°. - Cuboid

Find the dimensions of cuboid a, b, c; if diagonal d=9 dm has an angle with edge α=55° and has an angle with edge b β=58° - 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. - Prism diagonal

The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism? - Angle of deviation

The surface of the rotating cone is 30 cm² (with circle base), its surface area is 20 cm². Calculate the deviation of the side of this cone from the plane of the base. - Spherical section cut

Find the volume of a spherical section if the radius of its base is 10 cm and the magnitude of the central angle ω = 120 degrees. - Pyramid 8

Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°. - Calculate 36253

Calculate the volume of the pyramid, whose base edge a = 8 cm, and the sidewall makes an angle α = 60 ° with the square base. - Block

Calculate the volume of a cuboid ABCDEFGH if |AB| = 7 cm, |BC| = 8 cm and the angle ∠CDG = 30.1° - Deviation 70744

Calculate the volume and surface of the rotating cone if its height is 10 cm and the side has a deviation of 30 ° from the base plane. - 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 - Octagonal pyramid

Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.

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