# Problems of the cube

#### Number of problems found: 253

• The largest
We cut the largest possible cylinder from a 20 cm cube. What is the volume of this cylinder?
• The edge of a cube
How much does the edge of a cube of 54.9 cm3 measure?
• Surface of the cube
Find the surface of the cube that has volume 1/1m3 2/0.001 m3 3/8000 mm3
• Cuboid and ratio
Find the dimensions of a cuboid having a volume of 810 cm3 if the lengths of its edges coming from the same vertex are in ratio 2: 3: 5
• Wall thickness
The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
• Water container
The cube-shaped container is filled to two-thirds of its height. If we pour 18 liters, it will be filled to three-fifths of the height. What is the volume of the whole container?
• Container with water
The cube-shaped container is filled with water to half its height. If we add 20 liters of water, the container will be filled to three-quarters of its height. What is the volume of the whole container?
• One third power
Which equation justifies why ten to the one-third power equals the cube root of ten?
• 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?
• Length of the edge
Find the length of the edge of a cube with a cm2 surface and a volume in cm3 expressed by the same number.
• Surface area of a cube
What is the surface area of a cube that has an edge of 3.5?
• 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. )
• Water level
How many cm will the water level in a cube-shaped tank with an edge of 3 m drop if we discharge 189 hl of water?
• Wooden container
The locksmith should cover the cube-shaped wooden container with a metal sheet inside. The outer edge of the container is 54cm. The wall thickness is 25 mm. The container has no lid. Calculate. How many sheets will be needed to cover it?
• Dice and coin
A number cube is rolled and a coin is tossed. The number cube and the coin are fair. What is the probability that the number rolled is greater than 2 and the coin toss is head?
• Six speeds
A drilling machine is to have 6 speeds ranging from 50 to 750 revolutions per minute. If the speed forms a geometric progression, determine their values.
• Three members GP
The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
• Two cubes
The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
• Profit growth
The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods?
• The cube
The cube has an edge of 25 cm. We cut it into small cubes of 5 cm long side. How many of these little ones left when we build a new cube of 20 cm in length?

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