Solid geometry, stereometry - last page

Number of problems found: 2409

Big Earth
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km.
Regular quadrangular pyramid
How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge of 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%.
Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the cylinder's axis. How many hectoliters of water is in the cylinder?
Right-angled trapezoid
A right-angled trapezoid with the measure of the acute angle of 50° is given. The lengths of its bases are 4 and 6 units. The volume of the solid obtained by rotation of the given trapezoid about the longer base is:
Cone side
Calculate the volume and area of the cone whose height is 10 cm, and the axial section of the cone has an angle of 30 degrees between height and the cone side.
Pyramid - angle
Calculate the regular quadrangular pyramid's surface, the base edge of which is measured 6 cm, and the deviation from the plane of the base's sidewall plane is 50 degrees.
Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
Forces
In point, G acts three orthogonal forces: F₁ = 16 N, F₂ = 7 N, and F₃ = 6 N. Determine the resultant of F and the angles between F and forces F₁, F₂, and F₃.
Rotation of the Earth
Calculate the circumferential speed of the Earth's surface at a latitude of 34.5°. Consider a globe with a radius of 6378 km.

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