# Body volume - math word problems

1. Pool The pool has the shape of a cylinder with a diameter 4.6m, the presumed height is 130cm. The bucket fits 12l of water. How many buckets do you have to bring to fill this pool?
2. Triangular prism The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm2 and the body height is 10 cm. Calculate the body volume.
3. Cone Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
4. Cuboid - edges The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid
5. Hexagonal prism 2 The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.
6. The factory The factory ordered 500 hexagonal steel bars of square section with 25 mm side. How many cars with a load capacity of 3 tonnes will be needed for bars move if the steel density is 7,850 kg.m-3? The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.
8. Cube walls Find the volume and surface area of the cube if the area of one wall is 40cm2.
9. Pyramid in cube In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid.
10. Rotary bodies The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
11. The tent The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
12. Inscribed sphere How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?
13. Wall height Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
14. Axial cut The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
15. 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.
16. 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.
17. Rotating cone Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
18. Cube diagonals Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
19. Cuboid and ratio Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.
20. Cone The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?

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