# Body volume + expression of a variable from the formula - math problems

1. The tent
The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m2 of cloth we need to make the tent if we have to add 7% of the seams? How many m3 of air will be in the tent?
2. Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
3. Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
4. Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
5. Cuboid and ratio
Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.
6. Cylindrical tank
Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder.
7. Gasoline tank cylindrical
What is the inner diameter of the tank, which is 8 m long and contains 40 cubic cubic meters of gasoline?
8. The cylinder base
The cylinder with a base of 8 dm2 has a volume of 120 liters. From a cylinder fully filled with water, 40 liters of water was removed. At what height from the bottom /with precision to dm/ is the water level?
9. Cylinder twice
If the radius of the cylinder increases twice, and the height is reduced twice, then the volume of the cylinder increases (how many times?):
10. Prism - box
The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.
11. Cylinder
In a 1-meter diameter cylinder is 1413 liters of water, which is 60% of the cylinder. Calculate the cylinder height in meters, do not write the units. The resulting value round and write as an integer.
12. Tank diameter
A cylindrical tank has a volume of 60 hectoliters and is 2.5 meters deep. Calculate the tank diameter.
13. Cone container
Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
14. Prism
The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters?
15. Tent
Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
16. Tetrahedral prism
The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge, if you know that the prism volume is 2187 cm3.
17. Third dimension
Calculate the third dimension of the cuboid: a) V = 224 m3, a = 7 m, b = 4 m b) V = 216 dm3, a = 9 dm, c = 4 dm
18. Cube 7
Calculate the volume of a cube, whose sum of the lengths of all edges is 276 cm.
19. Aquarium 6
How high is the water level in the aquarium with a rectangular base 40cm and 50cm if it is filled 0,65hl of water?
20. Prism
The volume of tetrahedral prism is 2.43 m3. Base of prism is a parallelogram in which a side 2,5dm and height ha = 18cm. Calculate the height of the prism.

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