# Volume - 8th grade (13y) - examples - page 14

1. Equilateral cylinder A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
2. Find the Find the volume of a quadrangle prism high 2dm whose base is a square with a side 15cm.
3. Gasoline tank 2 A gasoline tank is 1/6 full. When 25 liters of gasoline were added, it became 3/4 full. How many liters more is needed to fill it? Show your solution.
4. Sand path How many m3 of sand is needed to fill the 1.5m wide path around a rectangular flowerbed of 8m and 14m if the sand layer is 6cm high?
5. Vehicle tank A vehicle tank was 3/5 full of petrol. When 21 liters of fuel was added it was 5/6 full. How many liters of petrol can the tank hold?
6. Three pumps We are filling the pool. The first pump would be filled in 12 hours, the second pump in 15 hours. If all three pumps were running at the same time, it would fill the pool for 4 hours. How long would the pool fill only with the third pump?
7. Square prism Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
8. Volume and body diagonal Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%?
9. Cube into sphere The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
10. 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?
11. 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.
12. 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)
13. 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
14. 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?
15. 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?
16. Bricks pyramid How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid?
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. 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.
20. 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

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