# 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.

1. Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
2. Truncated cone
A truncated cone has a base radius 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume.
The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.
4. Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
5. Cube
Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.
6. Pool in litres
Pool has a width of 3.5 m length of 6 m and a height 1.60 meters. Calculate pool volume in liters.
7. Concrete pedestal
The carpenters made wooden mold on a concrete pedestal in the shape of a cube with edge 2 meter long. What is the area in which the concrete touches wooden molds? (No lid or bottom)
8. 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.
9. Rainfall
On Thursday, fell 1 cm rainfall. How many liters of water fell to rectangular garden with dimensions of 22 m x 35 m?
10. Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
11. The cube
The surface of the cube is 150 square centimeters. Calculate: a- the content of its walls b - the length of its edges
12. Glass aquarium
How many m2 of glass are needed to produce aquarium with bottom dimensions of 70 cm x 40 cm and 50 cm high?
13. Billiard balls
A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
14. 3s prism
It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.
Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
16. Cuboid - edges
The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid
17. Truncated cone 5
The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone?
18. 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 De
19. Water channel
The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow
20. Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.

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