Solid geometry, stereometry

Solid geometry is the name for the geometry of three-dimensional Euclidean space.

Stereometry deals with 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: 956

Pyramid
Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
Pyramid roof
2/4 of area of the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
Tower
How many m² of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
Vector
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
Cuboid
Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
Task
I have homework. The cube has an edge 7 cm long and I must find wall and body diagonal.
Rotating cone II
Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
Rotary cone
Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm³. Calculate the radius of the base circle and height of the cone.
Tinsmith
Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add $x cm width of the plate?
Cube in a sphere
The cube is inscribed in a sphere with volume $V cm³. Determine the length of the edges of a cube.
Tank
In the middle of a cylindrical tank with a bottom diameter 251 cm is standing rod which is 13 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
Road embankment
Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?
Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm².
Gold wire
From one gram of gold was pulled wire 2.1 km length. What is it diameter if density of Au is ρ=19.5 g/cm³?
Cylinders
Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much?
Diagonal
Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
Felix
Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
Roller
Cylinder shell has the same content as one of its base. Cylinder height is 15 dm. What is the radius of the base of the cylinder?

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