Solid geometry, stereometry - page 120 of 123

Number of problems found: 2441

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.
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.
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.
Pyramid - angles
In a regular pyramid in which the edge of the base is | AB | = 4 cm; height = 6 cm, calculate the angle of the lines AV and CV, V = vertex.
Quadrilateral prism
The body diagonal of a regular quadrilateral prism forms an angle of 60° with the base. The edge of the base is 20 cm long. Calculate the volume of the body.
4side pyramid
Calculate the volume and surface of the regular four-sided pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
Cone
Calculate the volume and surface area of the cone with a diameter of the base d=16 cm and the side of the cone with the base has angle 37°12'.
Angle of two lines
There is a regular quadrilateral pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.
Calculate a cone
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.
Diagonal
Determine the dimensions of a cuboid whose space diagonal is 60 dm and makes an angle of 35° with one edge and 77° with another edge.
Glass of juice
A cylindrical glass 13 cm tall with a base diameter of 9 cm is filled with juice to a level 3 cm below the rim. Determine the maximum angle to which the glass can be tilted without the juice spilling.
9-sided pyramid
Calculate the surface area and volume of a regular nine-sided pyramid if the radius of the circle inscribed in the base measures ρ = 12 cm and the height of the pyramid is 24 cm
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.
Determine the surface area
Find the surface area of a cone of height 30 cm whose slant side makes an angle of 60° with the base plane.
Spherical section cut
Find the volume of a spherical section if the radius of its base is 10 cm and the magnitude of the central angle ω = 120 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.
Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid.
Calculate cuboid, diagonals
The volume of a cuboid with a square base is 64 cm³, and the space diagonal deviation from the base's plane is 45 degrees. Calculate its surface area.
Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism?
Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base

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