Cube + quadratic equation - practice problems
Number of problems found: 15
- Special cube
Calculate the cube's edge if its surface and volume are numerically equal numbers. - 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. - Smallest 79434
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - Cubes - diff
The second cube's edge is 2 cm longer than the edge of the first cube. Volume difference blocks are 728 cm³. Calculate the sizes of the edges of the two dice. - Derivative problem
The sum of two numbers is 12. Find these numbers if: a) The sum of their third powers is minimal. b) The product of one with the cube of the other is maximal. c) Both are positive, and the product of one with the other power of the other is maximal. - Equation 46771
Insert three numbers between the roots of the equation 4x² - 17x + 4 = 0 so that they form with the given GP numbers - Cubes
Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm². Determine the length of the edges of these cubes. - Two cubes
The surfaces of two cubes, one of which has an edge of 22 cm longer than the second, differ by 19272 cm². Calculate the edge length of both cubes. - 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? - Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube. - Assembling 63964
Little Pavel was assembling building blocks (a cube is shaped like a cube). He wanted to build a big cube. However, he had 75 dice left, so he increased the edge by one die. Then he was missing 16 dice. How many cubes did he have in the kit? - The pool
The cube-shaped pool has 140 cubic meters of water. Determine the bottom's dimensions if the water's depth is 200 cm and one dimension of the base is 3 m greater than the other. What are the dimensions of the pool bottom? - 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? - 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 - Rectangle pool
Find dimensions of an open pool with a square bottom with a capacity of 32 m³ to have painted/bricked walls with the least amount of material.
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