Examples for secondary school students - page 221 of 230
Number of problems found: 4586
- Wire D
Wire length 6 m is bent to form a semicircle circuit (including the diameter). Determine the radius of the semicircle. - Area of RT
The right triangle has orthogonal projections of legs to the hypotenuse lengths 15 cm and 9 cm. Determine the area of this triangle. - Square 2
Points D[10,-8] and B[1,-10] are opposed vertices of the square ABCD. Calculate the area of the square ABCD. - Square
Points A[9,9] and B[-4,1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD. - Gimli Glider
Aircraft Boeing 767 lose both engines at 35000 feet. The plane captain maintains optimum gliding conditions. Every minute, lose 2100 feet and maintain constant speed 201 knots. Calculate how long it takes for a plane to hit the ground from engine failure. - Triangle TBC
TBC is an isosceles triangle with base TB with base angle 75° and legs length |TC| = |BC| = 35. How long is the base TB? - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Forces
In point, G acts three orthogonal forces: F1 = 16 N, F2 = 7 N, and F3 = 6 N. Determine the resultant of F and the angles between F and forces F1, F2, and F3. - Diagonal
Determine the dimensions of the cuboid if it is diagonally long 60 dm and has an angle with one edge 35° and with another edge 77°. - Cone A2V
The cone's surface in the plane is a circular arc with a central angle of 126° and an area of 415 cm². Calculate the volume of a cone. - Axial section
The axial section of the cone is an equilateral triangle with an area 208 km². Calculate the volume of the cone. - Rotation
The right triangle with legs 11 cm and 18 cm rotates around the longer leg. Calculate the volume and surface area of the formed cone. - Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 5a +5b = 7c - Euclid3
Calculate the height and sides of the right triangle if one leg is a = 100 km and the section of hypotenuse adjacent to the second leg cb = 14 km. - Euclid2
The ABC right triangle with a right angle at C is side a=29 and height v=17. Calculate the perimeter of the triangle. - Euclid1
The right triangle ABC has hypotenuse c = 20 cm. How large sections cut height hc=9 cm on the hypotenuse c? - Hole
We will drill the cylinder shape hole in the cube's center with an edge 16 cm. The volume of the hole must be 10% of the cube. What should drill diameter be chosen? - Pyramid roof
3/5 of the area of the roof-shaped regular tetrahedral pyramid with base edge 9 m and height of 6 m is already covered with roofing. How many square meters still need to be covered? - Numbers
Determine the number of all positive integers less than 5965074 if each is divisible by 5, 29, 11. What is its sum? - Circles
The areas of the two circles are in the ratio 5:10. The larger circle has a diameter of 14. Calculate the radius of the smaller circle.
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