# Body volume - examples - page 19

1. Minimum surface Find the length, breadth, and height of the cuboid shaped box with a minimum surface area, into which 50 cuboid shaped blocks, each with length, breadth and height equal to 4 cm, 3 cm and 2 cm respectively can be packed.
2. Body diagonal Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
3. Circular pool The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
4. The coil How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
5. Annual rainfall The average annual rainfall is 686 mm. How many liters will fall on the 1-hectare field?
6. Cylindrical container An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
7. Cube surface and volume Find the surface of the cube with a volume of 27 dm3.
8. How much How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč?
9. Bricks pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
10. Cuboid walls If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
11. Pyramid cut We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
12. Children's pool Children's pool at the swimming pool is 10m long, 5m wide and 50cm deep. Calculate: (a) how many m2 of tiles are needed for lining the perimeter walls of the pool? (b) how many hectoliters of water will fit into the pool?
13. Water tank A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water.
14. Orlík hydroelectric plant The Orlík hydroelectric power plant, built in 1954-1961, consists of four Kaplan turbines. For each of them, the water with a flow rate of Q = 150 m3/s is supplied with a flow rate of h = 70.5 m at full power. a) What is the total installed power of the p
15. Regular triangular pyramid Calculate the volume and surface area of the regular triangular pyramid and the height of the pyramid is 12 centimeters, the bottom edge has 4 centimeters and the height of the side wall is 12 centimeters
16. Living room How many people can live in a room with dimensions: a = 4m b = 5m c = 2.5m if one person needs 15m cubic space (i. E. Air . .. )?
17. Butter At the Orville redenbocher popcorn factory there is a tank of artificial butter substitute which is 55 feet tall and 18 feet in diameter. How many gallons of artificial butter substitute can the tank contain?
18. Cube edges If the edge length of the cube increases by 50%, how does the volume of this cube increase?
19. Rainfall A rectangular garden of 25m in length and width 20m in width fall 4mm of water. Express by a fraction in basic form what part of the 60-hectolitre tank we would fill with this water.
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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