Solid geometry, stereometry - page 114 of 116
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: 2320
- Moon
We see the Moon from the perspective angle 28'. At the time of the full Moon, the Moon's radius is 1740 km. Calculate the mean distance of the Moon from the Earth. - Horizontal 6161
We have a horizontal tank shaped like a rainwater cylinder, 3.45 m long and 1.7 m wide. (only up to a height of 85 cm) - 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. - 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. - Sphere submerged in the cone
A right circular cone with a top width of 24 cm and an altitude of 8 cm is filled with water. A spherical steel ball with a radius of 3.0cm is submerged in the cone. Find the volume of water below the sphere. - 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. - Angle of deviation
The surface of the rotating cone is 30 cm² (with a circle base), and its surface area is 20 cm². Calculate the deviation of this cone's side from the base's plane. - Glass
How many glasses are needed to produce glass with a base of a regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm?
- 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. - Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees. - Deviation 70434
Frustum has the base radii of the figures r1 and r2: r1> r2, r2 = s, and if the side deviation from the base plane is 60°. Express the surface and volume of the cone frustum using its side s. - Quadrilateral 82146
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the body diagonal makes an angle of 66° with the base. - Chimney
The lower circumference of the chimney is 12.57 m, and the top circumference is 5.655 m. The slope of the walls is 87°. Find the height of the chimney.
- Cuboid
Find the dimensions of cuboids a, b, and c; if diagonal d=9 dm has an angle with edge α=55° and has an angle with edge b β=58° - Cuboid
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine the angle between the body diagonal and the base plane (round to degrees). - Cone
Calculate the volume and surface area of the cone with a diameter of the base d=15 cm and the side of the cone with the base has angle 52°. - 4side pyramid
Calculate the volume and surface of the regular four-sided pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees. - 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.
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