Solid geometry, stereometry - page 121 of 123

Number of problems found: 2441

Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the base plane is α = 60°.
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 3.0 cm is submerged in the cone. Find the volume of water below the sphere.
Calculate pyramid
Calculate the volume of the pyramid, whose base edge a = 8 cm and the sidewall makes an angle α = 60° with the square base.
Side deviation
A frustum has base radii r₁ and r₂ where r₁ > r₂, r₂ = s, and the slant side makes an angle of 60° with the base plane. Express the surface area and volume of the frustum in terms of its slant height s.
Vertex angle - cone
The rotating cone has a height of 72 cm and an angle at the top of 72°. Determine the volume of a sphere with the same radius as the cone.
Pyramid 8
Calculate the volume and the surface area of a regular quadrilateral pyramid with a base side of 9 cm and a side wall with the base has an angle of 75°.
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
Block
Calculate the volume of a cuboid ABCDEFGH if |AB| = 7 cm, |BC| = 8 cm and the angle ∠CDG = 30.1°
Pyramid
The pyramid has a base a = 2cm and height in v = 7 cm. a) calculate the angle between plane ABV and the base plane b) Calculate the angle between the edges on the opposite side.
Calculate cuboid
Given cuboid ABCDEFGH. We know that |AB| = 1 cm, |BC| = 2 cm, |AE| = 3 cm. Calculate in degrees the angle size formed by the lines BG and FH .
Pentagonal pyramid
Calculate the volume of a regular 5-side (pentaprism) pyramid ABCDEV; if |AB| = 6.7 cm and a plane ABV, ABC has angle 32 degrees.
Earth parallel
The Earth's radius is 6377 km. Calculate the circumference of the parallel at latitude 75°.
Square pyramid
Calculate the pyramid's volume with the side 5 cm long and with a square base, and the side base has an angle of 60 degrees.
Regular quadrangular pyramid
The height of the regular quadrilateral pyramid is 6 cm, and the length of the base is 4 cm. What is the angle between the ABV and BCV planes? ABCD is the base, V is the vertex.
Pentagonal prism
The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
Angle of cone
The cone has a base diameter of 1.5 m. The angle at the central apex of the axial section is 86°. Calculate the volume of the cone.
Cone
The rotating cone volume is 9.42 cm³, with a height of 10 cm. What angle is between the side of the cone and its base?
In a regular 5
In a regular triangular prism ABCV, the angle between the lateral face and the base plane is α = 45°. Determine the angle between the lateral edge and the base plane.
The hemisphere
The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
The roof
The tower's roof has the shape of a regular quadrilateral pyramid, the base edge of which is 11 m long, and the side wall of the animal with the base at an angle of 57°. Calculate how much roofing we need to cover the entire roof if we count on 15% waste.

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