Solid geometry, stereometry - page 122 of 123
Number of problems found: 2441
- Cube - angles
Calculate the angle alpha (α) between the face diagonal and the base of a cube. Calculate the angle beta (β) between the space diagonal and the base of the cube. - Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base is 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm³. - Box
Calculate the angle between the base of a cuboid with dimensions 5 × 10 and its space diagonal of length 13. - House volume
V = 35 m α = 55° β = 15° ----------------- X =? Calculate: V- barrack volume =? S- barrack area =? - House roof
The house's roof is a regular quadrilateral pyramid with a base edge 20 m. If the roof pitch is 38° and we calculate 12% of waste, connections, and overlapping of the area roof, how much m² is needed to cover the roof? - Cone slope
Determine the volume and surface area of a cone whose slope of length 8 cm makes an angle of 75 degrees with the plane of the base. - Pilot
How high can the airplane's pilot see 0.001 of Earth's surface? - Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c have dimensions in the ratio of 10:8:9. If you know that the diagonal wall AC is 75 cm, and the angle between AC and space diagonal AG is 30 degrees. - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the ball's surface and the area of the base is 4:3. A plane passing through the axis of a cone cuts the cone in an isosceles triangle - Felix
Calculate how much land Felix Baumgartner saw after jumping from 36 km above the ground. The radius of the Earth is R = 6378 km. - Tropical, mild and arctic
How many percent of the Earth's surface lies in the tropical, mild, and arctic ranges? The border between the ranges is the parallel 23°27' and 66°33'. - 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. - 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? - Regular quadrangular pyramid
How many square meters are needed to cover a regular quadrilateral pyramid base edge of 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%. - Cone side
Calculate the volume and lateral surface area of a cone with a height of 10 cm, given that the axial cross-section has an angle of 30° between the height and the slant side. - 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: - Pyramid - angle
Calculate the regular quadrilateral 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 the cone's dimensions. - Forces
At point G, three mutually perpendicular forces act: F₁ = 16 N, F₂ = 7 N, and F₃ = 6 N. Determine the resultant force F and the angles between F and each of F₁, F₂, and F₃.
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