Square root + body volume - examples

1. TV transmitter The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
2. Cube in a sphere The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
3. Axial section Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
4. Rectangular cuboid The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
5. Cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
6. Cubes One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
7. Sphere The surface of the sphere is 2820 cm2, and weight is 71 kg. What is its density?
8. Cone Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
9. Sandpile Auto sprinkled with sand to an approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the san
10. Rotation Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
11. Prism X The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
12. Cone Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
13. Balls Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
14. Gold wire From one gram of gold was pulled wire 2.1 km length. What is it diameter if density of Au is ρ=19.5 g/cm3?
15. Hole In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen? Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?
17. Rotary cone Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm3. Calculate the radius of the base circle and height of the cone.
18. Sphere A2V Surface of the sphere is 241 mm2. What is its volume?
19. Cube 6 Volume of the cube is 216 cm3, calculate its surface area.
20. 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.

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