Solid geometry, stereometry - page 118 of 121
Number of problems found: 2404
- 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. - Base diagonal
In a regular four-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the pyramid's surface area and volume. - 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. - 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. - Decagon prism
A regular decagon of side a = 2 cm is the base of the perpendicular prism. The side walls are squares. Find the prism volume in cm³, round to two decimal places. - Deviation of the lines
Find the deviation of the lines AG BH in the ABCDEFGH box-cuboid if given | AB | = 3cm, | AD | = 2cm, | AE | = 4cm - Angle of deviation
The surface of the rotating cone is 30 cm² (with a circle base), and its surface area is 20 cm². Calculate the deviation of this cone's side from the base's plane. - Calculate cuboid, diagonals
The volume of a cuboid with a square base is 64 cm3, and the body diagonal deviation from the base's plane is 45 degrees. Calculate its surface area. - Horizontal watertank
We have a horizontal tank shaped like a rainwater cylinder, 3.45 m long and 1.7 m wide. Calculate how many liters of water is in first centimeters. - 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? - Sphere submerged in the cone
A right circular cone with a top width of 24 cm and an altitude of 8 cm is filled with water. A spherical steel ball with a radius of 3.0cm is submerged in the cone. Find the volume of water below the sphere. - 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° - Calculate 3019
The height is 5 cm, and the size of the angle that the side of the cone with the base makes is 63 degrees. Calculate the surface and volume of this cone. - 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. - 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. - Cuboid
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine the angle between the body diagonal and the base plane (round to degrees). - Rotary cone
The volume of the rotation of the cone is 733 cm³. The angle between the side of the cone and the base angle is 75°. Calculate the lateral surface area of this cone. - Angle of two lines
There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - Calculate cone
The rotating cone has a base radius r = 226 mm, and the deviation of the side from the base plane is 56°. Calculate the height of the cone. - Sun rays
If the sun's rays are at an angle of 60°, then the famous Great Pyramid of Egypt (which is now 137.3 meters high) has a 79.3 m long shadow. Calculate the current height of the neighboring Chephren pyramid, whose shadow is measured at the same time at 78.8
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