Planimetrics + reason - math problems
Number of problems found: 132
From the square with the integer side, cut out the square with the integer side so that the residual area is 100. What is the longest possible side of the larger square?
- Wheel gear
A drive wheel of radius 2 is connected to a drive wheel of radius 1 by a pulley of length 17. What is the distance between the wheel axles?
- Poisson distribution - daisies
The meadow behind FLD was divided into 100 equally large parts. Subsequently, it was found that there were no daisies in ten of these parts. Estimate the total number of daisies in the meadow. Assume that daisies are randomly distributed in the meadow.
Charles built a tower of cubes with an edge 2 cm long. In the lowest layer there were 6 cubes (in one row) in six rows, in each subsequent layer always 1 cube and one row less. What volume in cm3 did the whole tower have?
- Mr Duma
Mr Duma recently inherited a rectangular plot, part of the estate left by his late father. The plot with the following dimensions: Length=2x+1;Width=x-1. Determine the formula, in terms of x, that best describes the area of the rectangular plot. He has pl
- Divide an isosceles triangle
How to divide an isosceles triangle into two parts with equal contents perpendicular to the axis of symmetry (into a trapezoid and a triangle)?
- Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level?
Harry Thomson bought a large land in the shape of a rectangle with a circumference of 90 meters. He divided it into three rectangular plots. The shorter side has all three plots of equal length, their longer sides are three consecutive natural numbers. Fi
- Ten persons
Ten persons, each person makes a hand to each person. How many hands were given?
- Poplar shadow
The nine-meter poplar casts a shadow 16.2 m long. How long does a shadow cast by Peter at the same time, if it is 1.4 m high?
- Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side?
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
How probable is a randomly selected three-digit number divisible by five or seven?
- Cardboard box
Peter had square cardboard. The length of the pages was an integer in decimetres. He cut four squares with a side of 3 dm from the corners and made a box out of it, which fit exactly 108 cubes with an edge 1 dm long. Julia cut four squares with a side of
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
- Rotaty motion
What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling?
- A drone
A flying drone aimed the area for an architect. He took off perpendicularly from point C to point D. He was at the height of 300 m above ABC's plane. The drone from point D pointed at a BDC angle of 43°. Calculate the distance between points C and B in me
- Mysterious area
The trapezoid ABCD is given. Calculate its area if the area of the DBC triangle is 27 cm2.
Vladimir likes to draw rectangles. Yesterday he created all rectangles that had sides in centimeters and a circumference of 18 cm. How many rectangles of different dimensions have been drawn?
- Irregular pentagon
A rectangle-shaped, 16 x 4 cm strip of paper is folded lengthwise so that the lower right corner is applied to the upper left corner. What area does the pentagon have?
Planimetrics - math problems. Reason - math problems.