# Volume - math word problems

Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
2. Three cubes
The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?
3. Cylinder horizontally
The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
4. Excavation
Excavation for the base of the cottage 4.5 m x 3.24 m x 60 cm. The excavated soil will increase its volume by one-quarter. Calculate the volume of excavated soil.
5. Container
The container has a cylindrical shape the base diameter 0.8 m and the area of the base is equal to the area of the wall. How many liters of water can we pour into the container?
6. Alcohol mixture
Three liters of 96 percent alcohol we set up a certain amount of distilled water to form a 54-percent alcohol. How many liters of distilled water were used?
7. Liter of gold
What weight does 1 dm3 of gold have? Gold density is 19,300 kg / m3
8. Cooling liquid
Cooling liquid is diluted with water in a ratio of 3:2 (3 parts by volume of coolant with 2 volumes of water). How many volumes of coolant must be prepared for a total 0.7 dm3 (liters) of the mixture?
9. The pool
The pool has a volume of 40 m3 and the water temperature is 20 °C. How much water at 100 °C should we pour into the pool to increase the water temperature by 5 °C?
10. Triangular prism
Calculate the volume and surface area of a triangular prism if it is given: a = 6.8 dm. ..Va = 4 dm. (base edge length and base triangle height length) ... ... .v = 23 dm (body height)
11. Cube wall
Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
12. Two cuboids
Find the volume of cuboidal box whose one edge is: a) 1.4m and b) 2.1dm
13. Clay
How many cubic centimeters of clay is in a pit of dimensions 4 m x 3 m x 3 m?
14. Gas consumption
The vessel consume 100 tons of gas in 250 miles. How many fuel will the vessel consume if it travels 400 miles?
15. One deci
Wine 0,375 l costs 2040 CZK. How much does 1 dl cost?
16. Trench
The trench is a four-sided prism. The cross section has a trapezoidal shape with basements of 4m and 6m, the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil.
17. Cuboid
Cuboid has a surface of 516 cm2. Side a = 6 cm and b = 12 cm. How long is the side c =?
18. Surface of cuboid
Find the surface of the cuboid if its volume is 52.8 cm3 and the length of its two edges is 2 cm and 6 cm.
19. Water channel
The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flo
20. Volume of cube
Solve the volume of a cube with width 26cm .

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