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.
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.
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.
- 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?
- 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.
Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m2 =.
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
- 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.
- Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
- 3sides prism
The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
- Bricks wall
There are 5000 bricks. How high wall thickness of 20 cm around the area which has dimensions 20 m and 15 m can use these bricks to build? Brick dimensions are 30 cm, 20 cm and 10 cm.
- 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
- Cube wall
Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
- Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
- Rotary cylinder
The rotating cylinder has a surface area 69.08 cm2. The area of the shell is 62.8 cm 2. What is the diameter of the cylinder?
How many liters of water per second can go via trough, which has a cross section of semicircle with radius 2.5 m and speed of water is 147 cm per second?
See also more information on Wikipedia.