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.

Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
Stadium
A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
Axial cut
The cone surface is 388.84 cm², the axial cut is an equilateral triangle. Find the cone volume.
Body diagonal
Find the cube surface if its body diagonal has a size of 6 cm.
Regular quadrilateral pyramid
Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
Truncated cone 3
The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang.
Cone
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?
Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
Trench
The trench is a four-sided prism. The cross section has a trapezoidal shape with basements of 4m and 6m, the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil.
Pyramid
The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
Quadrangular pyramid
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this.
Pyramid four sides
In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters.
Wall diagonal
Calculate the length of wall diagonal of the cube whose surface is 384 cm square.
The cylinder base
The cylinder with a base of 8 dm² has a volume of 120 liters. From a cylinder fully filled with water, 40 liters of water was removed. At what height from the bottom /with precision to dm/ is the water level?
Cube walls
Find the volume and surface area of the cube if the area of one wall is 40cm2.
Triangular prism
The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm² and the body height is 10 cm. Calculate the body volume.
Cone
Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.

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