Volume + surface area - math problems

1. 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.
2. Axial section Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
3. Rectangular cuboid The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
4. Cubes One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
5. Sphere The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
6. Cuboid diagonal Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
7. Rotation The right triangle with legs 14 cm and 20 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone.
8. Tetrahedral pyramid Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
9. Sphere slices Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
10. 4side pyramid Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees.
11. Pyramid a+h Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
12. Tetrahedral pyramid Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
13. Triangular pyramid Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
14. Hexagonal pyramid Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
15. Hexagonal prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
16. Mystery of stereometrie Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
17. Pit Pit has shape of a truncated pyramid with rectangular bases and is 0.8 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.6 l of green colour. How many liters of paint is needed when w
18. Cuboid Find the cuboid that has the same surface area as the volume.
19. Triangular prism Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.
20. Triangular prism Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.

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