# Third power - high school - examples

1. Calculate 3 Calculate the cube volume whose edge is 3x-1,3x-1,3x-1
2. Cube zoom How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
3. 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?
4. 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.
5. Hollow sphere Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
6. Equilateral cylinder Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
7. Cylinder - area The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m3.
8. Funnel The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water.
9. Surface of the cylinder Calculate the surface area of the cylinder when its volume is 45 l and the perimeter of base is three times of the height.
10. Variations 3rd class From how many elements we can create 13,800 variations 3rd class without repeating?
11. Two boxes-cubes Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge?
12. Tower model Tower height is 300 meters, weight 8000 tons. How high is the model of the tower weight 1 kg? (State the result in the centimeters). The model is made from exactly the same material as the original no numbers need to be rounded. The result is a three-digi
13. Rectangle pool Determine dimensions of open pool with a square bottom with a capacity 32 m3 to have painted/bricked walls with least amount of material.
14. Cube 9 What was the original edge length of the cube if after cutting 39 small cubes with an edge length 2 dm left 200 dm3?
15. Prism bases Volume perpendicular quadrilateral prism is 360 cm3. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
16. Cuboid edges in ratio Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
17. Body diagonal The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
18. Pyramid cut We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
19. Rate or interest At what rate percent will Rs.2000 amount to Rs.2315.25 in 3 years at compound interest?
20. Cube edges If the edge length of the cube increases by 50%, how does the volume of this cube increase?

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