# 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.

- Body diagonal

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

The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm^{3}. Calculate the surface of the prism. - 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? - Painting

The room is long 50 meters and wide 60dm and 300 cm high. Calculate how much it will cost painting if area of windows and doors is 15% of the total area. One square meter cost 50cents. - Concrete block

Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters. - Costume

Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand D - Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm. - Rainfall

How many liters of water did fell in a 32m long and 8m wide garden, if 8mm of rain fell? - Octahedron

All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron. - Cone container

Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package. - Lamp cone

Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm. - Truncated cone

A truncated cone has a bases radiuses 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume. - Shell of cylinder

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

The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters? - Triangular prism

Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume. - Bricks wall

There are 5000 bricks. How high wall thickness of 20 cm around the area which has dimensions 20 m and 15 m can use these bricks to build? Brick dimensions are 30 cm, 20 cm and 10 cm. - Prism

Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m. - Decagon prism

A regular decagon of side a = 2 cm is the base of the perpendicular prism, the side walls are squares. Find the prism volume in cm^{3}, round to two decimal places. - Hexa prism

Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm. - Prism - eq triangle

Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.

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