Solid geometry, stereometry - page 111 of 115
Solid geometry is the name for the geometry of three-dimensional Euclidean space.Stereometry involves 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.
Number of problems found: 2291
- Paper box
Calculate the paper consumption on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm, and the adjacent base edges form an angle alpha = 60 °. Box height is 10 cm. How much m² of the paper is consumed 100 such boxes? - Centroid - two bodies
A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi - Flowerbed
Flowerbed has the shape of a truncated pyramid. The bottom edge of the base a = 10 m, and the upper base b = 9 m. The deviation angle between the edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be plante - House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How much m² is needed to cover the roof if the roof pitch is 57° and we calculate 11% of waste, connections, and overlapping of area roof?
- Cross-section 62964
The owner must cover the carport with a hipped roof with a rectangular cross-section of 8 m x 5 m. All roof surfaces have the same slope of 30°. Determine the price and weight of the roof if 1 m² cost €270 and weighs 43 kg. - An Elizabethan collar
An Elizabethan collar is used to prevent an animal from irritating a wound. The angle between the opening (diameter 6 inches) with a 16-inch diameter and the side of the collar is 53 degrees. Find the surface area of the collar shown. - The cone
The cone's lateral surface area is 4 cm², and the area of the base is 2 cm². Find the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base circle. All sides of - Quadrilateral oblique prism
What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°? - Diagonals of a prism
The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal and the base's diagonal.
- Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C' has an angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism. - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Truncated pyramid
Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm, and the angle that the side wall with the base is 42 degrees. - Tetrahedral pyramid 8
Let all the side edges of the tetrahedral pyramid ABCDV be equally long, and its base let us be a rectangle. Find its volume if you know the deviations A=40° B=70° between the planes of adjacent sidewalls and the base plane. The height of the pyramid is h - Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm, and the diagonal body forms a 50-degree angle with the base plane.
- Glass
How many glasses are needed to produce glass with a base of a regular 5-gon if one base triangle in the base is 4.2 square cm and the height is 10 cm? - The spacecraft
The spacecraft spotted a radar device at an altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considere - Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - Horizontal Cylindrical Segment
How much fuel is in the horizontal cylindrical segment tank with a length of 10m, a width of level 1 meter, and a level is 0.2 meters below the tank's upper side? - Tower
How many m² of the copper plate should be replaced on the roof of the conical tower shape with a diameter 23 m, and the angle at the axial section's vertex is 119°?
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