Body volume + Pythagorean theorem - examples - page 3

1. Cuboid - volume, diagonals
The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid?
2. Support colum
Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.
3. Concrete block
Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters.
4. Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
5. Prism
Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m.
6. Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
8. 3s prism
It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.
9. Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
11. Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm.
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
14. Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this.
15. Cone
Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
16. Solid cuboid
A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has length 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
17. Ratio of edges
The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
Given is a regular quadrangular pyramid with a square base. The body height is 30 cm and volume V = 1000 cm³. Calculate its side a and its surface area.
19. Body diagonal
Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
20. Prism 4 sides
The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters

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Pythagorean theorem is the base for the right triangle calculator.