# Solid geometry, stereometry - page 19

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. Tower
How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
2. Gold wire
From one gram of gold was pulled wire 2.1 km length. What is it diameter if density of Au is ρ=19.5 g/cm3?
3. Regular quadrangular pyramid
How many square meters is needed to cover the tower the shape of regular quadrangular pyramid base edge 10 meters, if the deviation lateral edges from the base plane is 68 °? Calculate coverage waste 10%.
4. Axial section
Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
5. Pyramid - angle
Calculate the surface of regular quadrangular pyramid whose base edge measured 6 cm and the deviation from the plane of the side wall plane of the base is 50 degrees.
6. Tinsmith
Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add \$x cm width of the plate?
7. Cu wire
Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place.
8. Pool
Mr. Peter build a pool shape of a four-sided prism with rhombus base in the garden. Base edge length is 8 m, distance of the opposite walls of the pool is 7 m. Estimated depth is 144 cm. How many hectoliters of water consume Mr. Peter to fill the pool?
9. Cuboid
Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
10. Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
11. Cylinder
Calculate the dimensions of rotating cylindrical container with volume 2 l, if height of container is equal to the diameter of the base.
12. 4side pyramid
Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees.
Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?
14. Prism
Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 47 cm and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5.
15. Pyramid a+h
Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
16. Canopy
Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m2?
17. Rotary cone
Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3. Calculate the radius of the base circle and height of the cone.
18. Tetrahedral pyramid
Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
19. Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
20. 4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?

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