Pythagorean theorem + volume - practice problems - page 4 of 15
Number of problems found: 283
- Quadrilateral prism
The height of a regular quadrilateral prism is v = 10 cm, and the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the prism's volume. - Support colum
Calculate the support column's volume and surface, which is shaped as a vertical quadrangular prism whose base is a rhombus with diagonals u1 = 102 cm and u2 = 64 cm. Column height is 1. 5m. - Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them. - Tent
Calculate how many liters of air will fit in the tent with a shield in the shape of an isosceles right triangle with legs r = 3 m long, the height = 1.5 m, and a side length d = 5 m. - Triangular pyramid
Calculate a regular triangular pyramid's volume and surface area with a height equal to the base edge 10 cm long. - Quadrilateral 82146
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the body diagonal makes an angle of 66° with the base. - Calculate 5115
In the rotating cylinder, it is given: V = 120 cm3, v = 4 cm. Calculate r, S mantle. - The radius
A right circular cone's radius and slant heights are 9 cm and 15 cm, respectively. Find, correct to one decimal place, the (i) Height (ii) Volume of the cone - Base diagonal
In a regular 4-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the surface area and volume of the pyramid. - Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length of 3 cm and a height of 5 cm. - 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. - Determine 81311
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. - Quadrilateral 21523
Calculate the surface area and volume of a regular quadrilateral pyramid if the edge of the lower base is 18 cm and the edge of the upper base is 15 cm. The wall height is 9 cm. - ABCDA'B'C'D 6261
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. - Rotary bodies
The rotating cone and the rotary cylinder have the same volume of 180 cm³ and the same height, v = 15 cm. Which of these two bodies has a larger surface area? - Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C' has an angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism. - Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - Calculate 70634
The axial section of the cylinder is a rectangle with a diagonal of u = 20 cm. The height of the cylinder is twice the diameter of the base. Calculate the cylinder volume in liters. - 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 - Calculate 2548
Calculate the volume of a wooden box in the shape of a prism with the base of a rectangle if the box's width is 8 dm, the length is 14 dm, and the size of the body diagonal is 25 dm.
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