# 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.

- The diagram 2

The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm^{2}. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone - Spherical cap 4

What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula. - Pile of sand

A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand. - The pot

The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth. - Spherical cap

Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm^{2}. Determine the radius r of the sphere from which the spherical cap was cut. - 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? - Triangular pyramid

What is the volume of a regular triangular pyramid with a side 3 cm long? - Closed drum

Find the total surface area of a closed cylindrical drum if it's diameter is 50 cm and height is 45 cm . (π= 3.14) - Ribbon on the cube

A cubical gift box is tied with a piece of ribbon. If the total length of the free ends and the bow is 18 inches, what is the length of the ribbon used? (Each side of the cube is 6 inches). - Tetrahedral pyramid

Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m. - Diameter of a cylinder

The diameter of the cylinder is 42 cm. How many times does the cylinder turn on a 66m long track? - Tangent spheres

A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor an - Regular triangular pyramid

Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters - Quadrangular pyramid

The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area. - Cube cut

In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane. - Cuboidal room

Length of cuboidal room is 2m breadth of cuboidal room is 3m and height is 6m find the length of the longest rod that can be fitted in the room - Axial cut of a rectangle

Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long. - Iron density

Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3. - Octagonal tank

The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness. - Find diagonal

Find diagonal of cuboid with length=20m width=25m height=150m

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