Solid geometry, stereometry - page 22Solid 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.
- Center of the cube
Center of the cube has distance 33 cm from each vertex. Calculate the volume V and surface area S of the cube.
Calculate height and volume of a regular tetrahedron whose edge has a length 19 cm.
Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.
- Paper box
Calculate the consumption of paper on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm and the adjacent base edges forms an angle alpha = 60 °. Box height is 10 cm. How many m2 of the paper consumed 100 such boxes?
- Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
Roller has a diameter of 0.96 m and a width 169 cm. How many m2 of road level when he turns 42-times?
- 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.
- Quadrangular prism
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?
How many cubic centimeters of wood sawdust is created by cut the tree trunk with a diameter of 66 cm and when the gap width is 5 mm?
- Square pyramid
Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC.
- Spherical cap
What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
- The body
The body on the figure consists of cubes with an edge length 6 cm. What surface has this body?
- Building base
Excavation for the building base is 350x600x26000. Calculate its volume in m3.
- 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?
- 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?
- Cone container
Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
- Velocity ratio
Determine the ratio at which the fluid velocity in different parts of the pipeline (one part has a diameter of 5 cm and the other has a diameter of 3 cm), when you know that at every point of the liquid is the product of the area of tube [S] and the fluid.
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
See also more information on Wikipedia.