Pythagorean theorem - math word problems - page 54 of 73
Number of problems found: 1453
- Diagonals of a prism
The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal and the base's diagonal. - Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - Quadrilateral prism
Calculate the volume of a quadrilateral prism whose base is an isosceles trapezoid with bases 10 cm and 4 cm, 6 cm apart. The height of the prism is 25 cm. How could the surface area be calculated? - Base of prism
The base of the perpendicular prism is a rectangular triangle whose legs lengths are at a 3:4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm². - Pyramid - angles
In a regular pyramid in which the edge of the base is | AB | = 4 cm; height = 6 cm, calculate the angle of the lines AV and CV, V = vertex. - Lampshade
The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm² of material will we need when 10% is waste? - Prism and wall diagonal
The ABCDA'B'C'D' prism has a square base. The wall diagonal of the AC base is 9.9 cm long, and the body diagonal AC' is 11.4 cm long. Calculate the surface area and volume of the prism. - Quadrilateral prism
The body diagonal of a regular quadrilateral prism forms an angle of 60° with the base. The edge of the base is 20 cm long. Calculate the volume of the body. - Prism - box
The prism's base is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism. - Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid with a height equal to the base edge, which is 10 cm long. - 4side pyramid
Calculate the volume and surface of the regular four-sided pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees. - Cone
Calculate the volume and surface area of the cone with a diameter of the base d=16 cm and the side of the cone with the base has angle 37°12'. - School model
The beech school model of a regular quadrilateral pyramid has a base 20 cm long and 24 cm high. Calculate a) the surface of the pyramid in square decimeters, b) the mass of the pyramid in kilograms if the density of the beech is ρ = 0,8 g/cm³ - Pool whitewashing
The pool is in the shape of a vertical prism with a bottom in the shape of an isosceles trapezoid with dimensions of the bases of the trapezoid 10m and 18m, and arms 7m are 2m deep. During spring cleaning, the bottom and walls of the pool must be whitewas - Regular 4BH
A regular quadrilateral prism has a volume of 864 cm³ and the area of its surface is twice the area of its base. Determine the size of its body diagonal. - Spherical bowl
The bowl, in the shape of part of a spherical surface, has a diameter of 28 cm at the top edge and is 8 cm deep. What is the total volume of the bowl? How much water would you have to pour into the bowl to fill it halfway? - Quadrilateral pyramid
The volume of a regular quadrilateral pyramid is 72 cm³. Its height is equal to the length of the base edge. Calculate the length of the base and the surface of the pyramid. - Slant surface
The surface of the rotating cone and its base area is in the ratio 18:5. Determine the volume of the cone if its body height is 12 cm. - Cone sphere volume A sphere is inscribed in an equilateral cone with a base diameter of 12 cm. Calculate the volume of both bodies. What percentage of the volume of the cone is filled by the inscribed sphere?
- The roof
The house's roof has the shape of a regular quadrilateral pyramid 5 m high and the edge of the base 7 m. How many tiles with an area of 540 cm² are needed?
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