Reason + diagonal - practice problems
Number of problems found: 27
- Tetrahedron 83144
A container shaped like a rotating cylinder with a base radius of 5 cm is filled with water. If a regular tetrahedron with an edge of 7 cm is immersed in it, how much will the water level in the container rise? - Dimensions 81670
A wooden crate with dimensions d=3m, e=4m, and f=3m was placed in a transport container with dimensions a=10 m, b=4m, and c=3m. What is the maximum length of a straight, rigid rod of negligible diameter that can still be placed in the container in this si - Quatrefoil 81138
Gothic quatrefoil is an ornament in which four identical touching smaller circles are inscribed in a larger circle, as you can see in the picture. The radius of the great circle is one meter. Calculate the radius of the smaller circle in meters. - Quadrilateral 81097
The quadrilateral ABCD is symmetrical about the diagonal AC. The length of AC is 12 cm, the length of BC is 6 cm, and the interior angle at vertex B is right. points E and F are given on the sides AB, and AD so that the triangle ECF is equilateral. Determ - Parallelogram 80761
Construct a parallelogram ABCD if a=5 cm, height to side a is 5 cm, and angle ASB = 120 degrees. S is the intersection of the diagonals. - Inaccessible 69794
Determine the distance between two inaccessible places P, Q, if the distance between two observation points A, B is 2000m and if you know the size of the angles QAB = 52°40''; PBA = 42°01''; PAB = 86°40'' and QBA = 81°15''. The considered locations A, B, - Competition 33041
The long-term volleyball tournament is played on a one-on-one basis. So far, 11 teams have entered the competition. How many matches will be lost when two teams unsubscribe? - Other's 31461
There are 13 guests at each other's party. How many clicks will you hear? - Ten persons
Ten persons, each person, make a hand to each person. How many hands were given? - Construct 10921
Construct the diamond ABCD so that its diagonal BD is 8 cm and the distance of apex B from the line AD is 5 cm. Specify all options - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an - Each with each
Five pupils from 3A class played table tennis. How many matches did they play with each other? - Perpendicular 7223
In the ABCDEFGHIJKL, the two adjacent sides are perpendicular to each other, and all sides except the AL and GF sides are identical. The AL and GF parties are twice as long as the other parties. The lines BG and EL intersect at point M. The quadrilateral - Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Equilateral 6306
We composed the diamond of four equilateral triangles with a side length of 7 cm. What's his circuit? - Rhombus 29
One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus. - ABCD square
In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Isosceles 5856
How many isosceles triangles form in a square when we mark all diagonals? - Calculate 4842
The area of the rotating cylinder shell is half the area of its surface. Calculate the surface of the cylinder if you know that the diagonal of the axial section is 5 cm. - Numerically 4839
Calculate the diagonal of such a square, for which it holds that its area is equal to its perimeter (without considering units, numerically ...).
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