# 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. Axial section
Axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
2. Diagonal
Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
3. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
4. Rotation
The right triangle with legs 11 cm and 18 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone.
5. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
6. Pyramid roof
2/4 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
7. Forces
In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
8. 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°
9. 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?
10. Felix
Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
11. Rainfall
Annual rainfall in our country are an average of 797 mm. How many m3 of water rains on average per hectare?
12. Rotating cone II
Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
13. Box
Calculate the angle between box base 9 x 14 and body diagonal length 18.
14. 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?
15. Earth parallel
Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
16. Sphere cuts
At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
17. Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
18. Cylinder
Calculate the dimensions of rotating cylindrical container with volume 2 l, if height of container is equal to the diameter of the base.
19. Cap
Jesters hat is shaped by a rotating cone. Calculate how much paper is needed to the cap 54 cm high when the head circumference is 47 cm.
20. Glass of juice
Glass of juice shaped cylinder 16 cm height and base diameter of 7 cm is filled with juice so that the level is 4 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...