Solid geometry, stereometry - page 120 of 121
Number of problems found: 2404
- 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? - Earth parallel
Earth's radius is 6377 km long. Calculate the length parallel to latitude 75°. - The roof
The tower's roof has the shape of a regular quadrangular 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. - 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. - 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 box base 9 x 14 and body diagonal length 18. - Cube - angles
Calculate the angle alpha (α) between the wall diagonal and cube base. Calculate the angle beta (β) between the cube body diagonal and the cube base. - 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? - Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes. - 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. - Pilot
How high can the airplane's pilot see 0.001 of Earth's surface? - 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 - Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube. - 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. - 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. - 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 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%. - 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.
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