Solid geometry, stereometry - page 117 of 121
Number of problems found: 2409
- 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°? - Reflector
The circular reflector throws a light cone with a vertex angle 56° and is on 24 m height tower. The axis of the light beam has the axis of the tower angle 11°. What is the maximum length of the illuminated horizontal plane? - Eight blocks
Dana had the task of saving the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be fo - 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 30 degrees, |AB| = 15 cm. Calculate the volume of the prism. - Chimney
The lower circumference of the chimney is 12.57 m, and the top circumference is 5.655 m. The slope of the walls is 87°. Find the height of the chimney. - Angle of diagonal
The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume. - Diagonal
Determine the dimensions of the cuboid if it is diagonally long 60 dm and has an angle with one edge 35° and with another edge 77°. - Glass of juice
The glass of juice-shaped cylinder 13 cm height and base diameter of 9 cm is filled with juice so that the level is 3 cm below the rim of the glass. Determine the maximum angle of the cup that we can tilt so the juice doesn't overflow. - Quadrilateral prism
The height of a regular quadrilateral prism is v = 10 cm, and the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the prism's volume. - 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. - Spherical sector
The spherical sector has axial section has an angle of α = 120° in the center of the sphere, is part of a sphere with a radius r = 10 cm. Calculate the surface of this spherical sector. - Quadrilateral prism
Calculate the volume (V) and the surface (S) of a regular quadrilateral prism whose height is 28.6 cm and the deviation of the body diagonal from the base plane is 50°. - Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - Cuboid
Find the dimensions of cuboids a, b, and c; if diagonal d=6 dm has an angle with edge α=35° and has an angle with edge b β=66° - Quadrilateral pyramid
The height of a regular quadrilateral pyramid is 6.5 cm, and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body—round calculations to 1 decimal place. - 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°? - Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees. - 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. - Moon
We see the Moon from the perspective angle 28'. At the time of the full Moon, the Moon's radius is 1740 km. Calculate the mean distance of the Moon from the Earth. - 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 of 0.2 meters below the tank's upper side?
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