Geometry - math word problems - page 158 of 162
Number of problems found: 3232
- 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°. - Vectors
Find the magnitude of the angle between two vectors u = (3; -5) and v = (10; 6) - Spherical section cut
Find the volume of a spherical section if the radius of its base is 10 cm and the magnitude of the central angle ω = 120 degrees. - Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base - 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. - Flowerbed
The flowerbed has the shape of a truncated pyramid. The bottom edge of the base a = 10 m, and the upper base b = 9 m. The deviation angle between the edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be pl - 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. - Decagon prism
A regular decagon of side a = 2 cm is the base of the perpendicular prism. The side walls are squares. Find the prism volume in cm³, round to two decimal places. - Perpendicular direction
A speedboat moves relative to the water at a constant speed of 13 m/s. The speed of the water current in the river is 5 m/s a) At what angle concerning the water current must the boat sail to keep moving perpendicular to the banks of the river? b) At what - Angle of two lines
There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - 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. - Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism? - Base RR odd
The base of the prism is an isosceles trapezoid ABCD with bases AB = 12 cm, and CD = 9 cm. The angle at vertex B is 48° 10'. Determine the volume and area of the prism if its height is 35 cm. - 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. - 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? - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and whose body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Cross-section of a roof
The owner must cover the carport with a hipped roof with a rectangular cross-section of 8 m x 5 m. All roof surfaces have the same slope of 30°. Determine the price and weight of the roof if 1 m² cost €270 and weighs 43 kg. - Block
Calculate the volume of a cuboid ABCDEFGH if |AB| = 7 cm, |BC| = 8 cm and the angle ∠CDG = 30.1° - Regular quadrangular pyramid
The height of the regular quadrangular 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. - 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.
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