Solid geometry, stereometry - page 120 of 121
Number of problems found: 2402
- House roof
The house's roof is a regular quadrangular 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? - Deviation - slope angle
Calculate the volume and surface of the rotating cone if its height is 10 cm and the side has a deviation of 30° from the base plane. - Side deviation
Frustum has the base radii of the figures r1 and r2: r1> r2, r2 = s, and if the side deviation from the base plane is 60°. Express the surface and volume of the cone frustum using its side s. - 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. - Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes. - 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 . - 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
- 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'. - Pilot
How high can the airplane's pilot see 0.001 of Earth's surface? - 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. - In a regular 5
In a regular triangular prism ABCV, the deviation of the side wall and the base plane is α = 45°. Determine the deviation of the side edge and the base plane. - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - 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? - 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.
- 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. - 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. - 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. - 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.
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