# Examples for secondary school students

#### Number of problems found: 2028

• Truncated cone 3 The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang.
• A cylinder A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
• Equation of circle 2 Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
• Medians of isosceles triangle The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
• Double probability The probability of success of the planned action is 60%. What is the probability that success will be achieved at least once if this action is repeated twice?
• Four sides of trapezoid In the trapezoid ABCD is |AB| = 73.6 mm; |BC| = 57 mm; |CD| = 60 mm; |AD| = 58.6 mm. Calculate the size of its interior angles.
• Circles The areas of the two circles are in the ratio 2:20. The larger circle has a diameter 20. Calculate the radius of the smaller circle.
• Larger perimeter There are a square and a circle that passes through two adjacent vertices of the square (end points of side a) and the center of the opposite side (c). Which of the plane shape has a larger perimeter?
• Cylinder and its circumference If the height of a cylinder is 4 times its circumference c, what is the volume of the cylinder in terms of its circumference, c?
• Euclid3 Calculate height and sides of the right triangle, if one leg is a = 81 cm and section of hypotenuse adjacent to the second leg cb = 39 cm.
• Height of the arc - formula Calculate the height of the arc if the length of the arc is 77 and chord length 40. Does exist a formula to solve this?
• Repair company The company repairs cars. The first day repair half of the contract second day, the half of the rest and third day 8 residue cars. How many total cars company repaired?
• Euclidean distance Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
• Rotation of the Earth Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
• Skid friction Find the smallest coefficient of skid friction between the car tires and the road so that the car can drive at a 200 m radius at 108 km/h and does not skid.
• Circle annulus There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
• Diamond diagonals Calculate the diamond's diagonal lengths if its content is 156 cm2 and the side length is 13 cm.
• Components In the box are 8 white, 4 blue and 2 red components. What is the probability that we pull one white, one blue and one red component without returning?
• Neighborhood I have 7 cups: 1 2 3 4 5 6 7. How many opportunities of standings cups are there if 1 and 2 are always neighborhood?
• V-belt Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm

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