# Volume - math word problems

1. Conical bottle When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
2. Milk There were 22 liters of milk in three containers. There was 6 liters more in the first container than in the second. After pouring 5 liters from the first container into the third container, the same quantity of milk is in the second and third container.
3. A plasticine Jožko modeled from plasticine. He used 27g of plasticine to model a 3 cm long cube. How many grams of plasticine will it need to mold cubes with an edge of 6cm?
4. Axial section of the cone The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
5. Cone side Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
6. Length of the edge Find the length of the edge of a cube that has a cm2 surface and a volume in cm3 expressed by the same number.
7. A square base A solid right pyramid has a square base. The length of the base edge is 4 centimeters and the height of the pyramid is 3 centimeters. What is the volume of the pyramid?
8. Cylinder The 1.8m cylinder contains 2000 liters of water. What area (in dm2) of this container is the water?
9. Octagonal pyramid Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
10. Tetrahedral pyramid Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
11. Uboid volume Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
12. Swimming pool The swimming pool has the shape of a block with dimensions of 70dm, 25m, 200cm. How many hl of water can fit into the pool?
13. Tributaries The pool can be filled with two different tributaries. The first inflow would fill the pool in 18 hours, both in 6 hours. How many hours would the pool filled with a second inflow?
14. Pouring alcohol 100 liters of alcohol has 70% How many liters of water need to be added to have 60% alcohol?
15. A filter It is a pool with a volume of 3500 liters. The filter filters at 4m cubic per hour. How many minutes would it filter the entire pool?
16. Cube construction A 2×2×2 cube is to be constructed using 4 white and 4 black unit cube. How many different cubes can be constructed in this way? ( Two cubes are not different if one can be obtained by rotating the other. )
17. The wellbore The wellbore has a tributary of 2 m3 per hour. When there is no tapping, there are a stable 28 liters of water in the well. The pump suction basket is at the bottom of the well. At 14.00, the water was pumped out at a rate of 0.5 liters of water every se
18. Two cylinders Two cylinders are there one with oil and one with an empty oil cylinder has no fixed value assume infinitely. We are pumping out the oil into an empty cylinder having radius =1 cm height=3 cm rate of pumping oil is 9 cubic centimeters per sec and we are p
19. The tax The tax per gallon of gasoline in California is \$0.477. If you fill your gasoline tank with 14.4 gallons of gasoline in California, how much will you pay in taxes? Round to the nearest cent.
20. Blueberries collecting Marie collects blueberries 2 l in 1 hour. Began collecting at 8.00 pm, Joe collects 1.5 l in 1 hour. Peter 1 l for 1 hr. And they began to gather at 08.30 pm. Together they collect 10 l. At what time will they all have collected?

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