Solid geometry, stereometrySolid 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: 1133
- 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°.
Pyramid has a base a = 3cm and height in v = 15 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
Calculate the volume of a cuboid ABCDEFGH if |AB| = 7 cm, |BC| = 8 cm and the angle ∠CDG = 30.1°
- 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 the angle between box base 9 x 14 and body diagonal length 18.
- Cube - angles
Calculate the angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
- 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.
How many glass are needed to produce glass with base regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
- 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.
- 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.
- 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.
- 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?
- Deviation of the lines
Find the deviation of the lines AG, BH in the ABCDEFGH box-cuboid, if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm
- Rotary cone
The volume of the rotation of the cone is 472 cm3, and the angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone.
- 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
- 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.
- Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also
- 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?
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