# Solid geometry, stereometry - page 27

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.

- Hexagonal prism 2

The regular hexagonal prism has a surface of 140 cm^{2}and height of 5 cm. Calculate its volume. - Shell of cylinder

Calculate the content of shell the 1.6 m height cylinder with a base radius of 0.4 m. - Church roof 2

The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m^{2}of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste? - Cuboid easy

The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid. - Roof 8

How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof. - Body diagonal

Find the cube surface if its body diagonal has a size of 6 cm. - Axial cut

The cone surface is 388.84 cm^{2,}the axial cut is an equilateral triangle. Find the cone volume. - 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. - Cube in sphere

The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere. - Cone

The rotating cone volume is 9.42 cm^{3,}with a height 10 cm. What angle is between the side of the cone and its base? - 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. - 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. - 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. - Wall diagonal

Calculate the length of wall diagonal of the cube whose surface is 384 cm square. - 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 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. - 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. - The cylinder base

The cylinder with a base of 8 dm^{2}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? - Body diagonal

The cuboid has a volume of 32 cm^{3.}Its side surface area is double as one of the square bases. What is the length of the body diagonal?

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