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.

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
Tank
In the middle of a cylindrical tank with a bottom diameter 251 cm is standing rod which is 13 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
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.
Prism
Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cub
Vector
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
Spherical segment
Spherical segment with height h=5 has a volume V=117. Calculate the radius of the sphere of which is cut this segment.
Prism
Three cubes are glued into prism, sum of the lengths of all its edges is 115 cm. What is the length of one edge of the original cube?
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.
Cylinder - h
Cylinder volume is 215 cm³. Base radius is 2 cm. Calculate the height of the cylinder.
4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
Pillar
Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.
Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
Prism
The lenght, width and height of a right prism are 17, 11 and 11 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
Logs
Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
Cylinders
Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much?
Spherical cap
From the sphere of radius 13 was truncated spherical cap. Its height is 6. What part of the volume is spherical cap from whole sphere?
Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
Cube in a sphere
The cube is inscribed in a sphere with volume 7253 cm³. Determine the length of the edges of a cube.
Cone
Circular cone of height 15 cm and volume 5699 cm³ is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
Cuboid
Cuboid with edge a=6 cm and body diagonal u=31 cm has volume V=900 cm³. Calculate the length of the other edges.

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