Square root + third power - practice problems - last page
Number of problems found: 39
- Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large - 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. - Block-shaped 7976
A block-shaped pool with a volume of 200m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³.
- 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 an area of 10 cm². Find the area of the or - Surface area 6156
The area (surface of the shell) of the cube is 93 cm². What is the volume of the cube? - Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double that of one of the square bases. What is the length of the body diagonal? - Rectangle pool
Find the dimensions of an open pool with a square bottom and a capacity of 32 m³ that can have painted/bricked walls with the least amount of material. - Determine 3888
Determine the sum of the three-third roots of the number 64.
- Four-thirds 3852
Anton said: I have a natural number x. I'll get three times as much if I increase it to four-thirds. What number did Anton mean? - Volume and area
What is a cube's volume with an area of 361 cm²? - Infinitely 3818
We have 2 numbers. If we multiplied the first number's third root by the second number's square root, we would get the number 18. Determine these 2 numbers. Calculate only the integer solution if the problem has infinitely many solutions in the set of rea - Equation: 3726
Determine the real root of the equation: x-3: x-8 = 32 - The cube
The cube has a surface area of 486 m². Calculate its volume.
- Cube 6
The surface area of one wall cube is 1600 cm square. How many liters of water can fit into the cube? - Prism X
The prism with the edges of the lengths x cm, 2x cm, and 3x cm has a volume 29478 cm³. What is the area of the surface of the prism? - Balls
Three metal balls with volumes V1=81 cm3, V2=96 cm3, and V3=28 cm³ were melted into one ball. Determine its surface area. - Sphere
The sphere's surface is 28500 cm², and the weight is 34.2 kg. What is its density? - Sphere A2V
The surface of the sphere is 241 mm². What is its volume?
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