# Square + cube - practice problems

#### Number of problems found: 92

- Sq and cube

Find the product of the square of (1/2) and the cube of (2/3) - Annual growth

The population has grown from 25,000 to 33,600 in 10 years. Calculate what was the average annual population growth in%? - 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. - One third power

Which equation justifies why ten to the one-third power equals the cube root of ten? - 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. - 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? - Power

Number left(sqrt(14 * sqrt[ 4 ] (14)) right)^{ 17 }can be written in the form 14^x. Find the value of x. - Root

Use law of square roots roots: cbrt (sqrt[2] (sqrt[4] (6))) = sqrt[n] (6) - 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 - Bricks pyramid

How many 50cm x 32cm x 30cm brick needed to built a 272m x 272m x 278m pyramid? - Cube-shaped container

The cube-shaped container has a height of 52 cm and a square base. The container was filled to the brim with water, then we immersed a metal cube in it, which caused 2.7 l of water to flow out of the container. After removing the cube from the water, the - Cubes

One cube is an inscribed sphere and the other one described. Calculate the difference of volumes of cubes, if the difference of surfaces in 231 cm². - 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. - Cube in a sphere

The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - Regular square prism

The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1: 3. Calculate the surface of the prism. - Cube cut

In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane. - 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 the surface of the prism? - Prism

Right-angled prism, whose base is a right triangle with leg a = 3 cm and hypotenuse c = 13 cm, has the same volume as a cube with an edge length of 3 dm. a) Find the height of the prism b) Calculate the surface of the prism c) What percentage of the cube' - Truncated cone 6

Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.

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Square practice problems. Cube practice problems.