# Solid geometry, stereometry - page 96 of 97

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: 1939

- 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, and the edge length is 10 cm. What is the volume of the prism? - 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°. - 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°. - 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. - The roof

The tower's roof 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 at an angle of 57°. Calculate how much roofing we need to cover the entire roof if we count on 15% waste. - Block

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

The rotating cone volume is 9.42 cm^{3}, with a height 10 cm. What angle is between the side of the cone and its base? - Pyramid

Pyramid has a base a = 3cm and height in v = 15 cm. a) calculate the angle between plane ABV and the base plane b) calculate the angle between opposite side edges. - 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. - Pentagonal prism

The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism. - Angle of cone

The cone has a base diameter of 1.5 m. The angle at the main apex of the axial section is 86°. Calculate the volume of the cone. - Regular quadrangular pyramid

The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes? - The hemisphere

The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees? - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}, and the angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - Earth parallel

Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°. - 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.

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