# Right triangle + body volume - math problems

1. 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?
2. A concrete pedestal A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
3. Tetrahedral pyramid A regular tetrahedral pyramid is given. Base edge length a = 6.5 cm, side edge s = 7.5 cm. Calculate the volume and the area of its face (side area).
4. Secret treasure Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
5. Body diagonal Calculate the volume of a cuboid whose body diagonal u is equal to 6.1 cm. Rectangular base has dimensions of 3.2 cm and 2.4 cm
6. Space diagonal The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
7. Base of prism The base of the perpendicular prism is a rectangular triangle whose legs length 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.
8. Lateral surface area The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
9. Pyramid height Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
10. The diagram 2 The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
11. Triangular pyramid What is the volume of a regular triangular pyramid with a side 3 cm long?
12. Triangular prism Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
13. Cube cut In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
14. 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 The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area.
16. Prism diagonal The body diagonal of a regular square prism has an angle of 60 degrees with the base, the edge length is 10 cm. What is the volume of the prism?
17. Axial cut of a rectangle Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
18. Perpendicular prism Calculate the volume of the perpendicular prism if its height is 60.8 cm and the base is a rectangular triangle with 40.4 cm and 43 cm legs.
19. Tetrahedral pyramid Calculate the surface S and the volume V of a regular tetrahedral pyramid with the base side a = 5 m and a body height of 14 m.
20. Cube diagonals Calculate the length of the side and the diagonals of the cube with a volume of 27 cm3.

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