# 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.

1. Hexagon cut pyramid Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
2. Diameter What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
3. Juice box The juice box has a volume of 200ml with its base is an isosceles triangle with sides a = 4,5cm and a height of 3,4cm. How tall is the box?
4. The tank The tank has 1320 liters of water. The tank has the shape of a prism, its base is an rectangle with sides a = 0,6 m and b = 1,5 m. How high does the water level reach in the tank?
5. Angle of deviation The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
6. Hexagonal prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
7. Nice prism Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
8. Children pool The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm. A) How many liters of water can fit into the pool? B) The pool is made of a double layer of plastic film
9. Square prism Calculate the volume of a square prism of high 2 dm wherein the base is: rectangle with sides 17 cm and 1.3 dm
10. Triangular prism Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides 6 cm 8 cm and 8 cm The quadrangular prism has a volume 648 cm3. Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism?
12. Surface area Calculate the surface area of a four-sides 2-m high prism which base is a rectangle with sides 17 cm and 1.3 dm
13. Painting To paint the pool with dimensions: 2 meters depth, 3m x 4m we bought paint to 50 meters square. How many "paint" will be a waste?
14. Megapascals What is the area of crosssection of the piston, if the force of 300 kN produces a pressure of 5 MPa?
15. Rope How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?
16. Cube in sphere The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
17. Sun rays If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current he
18. 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)
19. Rainfall On Thursday, fell 1 cm rainfall. How many liters of water fell to rectangular garden with dimensions of 22 m x 35 m? 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?