Volume - math word problems - page 22

1. Cube into sphere The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
2. The tank The tank is full up to 4/5 of the total height and contains 240 hl of water. The area of the base is 6 square meters. What is the height of the tank?
3. 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.
4. Fruit juice Fruit juice contains 37.5% sugar. How many percents of sugar will be in the flavored mineral that we prepare from 100 grams of fruit juice and 1.4 liters of mineral? (1 liter = 1 kg)
5. Body diagonal Calculate the volume and surface of the cube if the body diagonal measures 10 dm.
6. Circular pool The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
7. 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
8. Inlet and outlet The pool has a capacity of 50 hl. The inlet pipe flows in 1 minute 1.25 hl, and the waste pipe outlet is draining the full pool in 50 minutes. How long will take the empty the full pool when both the inlet and outlet are opened at the same time?
9. Five inlets The tank can be filled with five equally powerful inlets. If the tank is filled by four of these inlets, it takes a total of 30 minutes to fill one-third of the tank. How many minutes does it take to fill an empty tank if it is filled with all five inlets?
10. Annual rainfall The average annual rainfall is 686 mm. How many liters will fall on the 1-hectare field?
11. 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.
12. How much How much money will we pay for 20 planks 4m long, 15cm wide and 26mm thick when 1m³ of wood costs 4500kč?
13. Bricks pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
14. 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
15. 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.
16. 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?
17. Two pipes How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
18. Peroxide How many ml 30% of peroxide (H2O2) should be poured into 100ml H2O to give a 20% solution?
19. 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
20. 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.

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