Solid geometry, stereometry - page 90 of 92Solid 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
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)
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°.
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.
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°.
See also more information on Wikipedia.