# The most difficult problems

- Angle of two lines

There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - Equilateral triangle vs circle

Find the area of an equilateral triangle inscribed in a circle of radius r = 9 cm. What percentage of the circle area does it occupy? - A photograph

A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm². Find the size of paper and photo. - Castle model

The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm² of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of woo - Wheel turns

The diameter of the motorcycle wheel is 55 cm. How many times does a motorcycle wheel turn on a 5 km long road? - The difference

The difference of two numbers is 1375. If their exact quotient is 12. Find the two numbers - Three gardens

Is it possible to divide a plot of land with an area of 920 m² into three gardens in a ratio of 4: 2: 3 so that their areas are only whole multiples of square meters? - Pile of sand

A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sandpile is 31 feet. Find the volume of the pile of sand. - A screen

A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size? - Hyperbola equation

Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] - Coordinates of square vertices

The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square. - Closed drum

Find the total surface area of a closed cylindrical drum if it's diameter is 50 cm and height is 45 cm. (π= 3.14) - A metal

A metal cylinder is inserted into the cube with a 20 cm edge so that the cylinder shell and its two bases are in close contact with the walls of the cube from the inside. How much water could be poured into the free space between the cube and the cylinder - KLM triangle

Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees. - The size

The size of a Trapezium are 3/4×cm, ×cm 2(×+1)cm and 3(×+2)cm long respectively if it's perimeter is 60cm, calculate the length of each side. - Sum of dividend

Suppose X is divided separately 2.63 and 1.40. And the results of the individual divisions are added to give a result less than X. What is X? - Unknown mixed number

Find the number that is smaller than 5 5/12 by as much as 2 2/13 is smaller than 6 1/6 - Calculate 3

Calculate the cube volume whose edge is 3x-1,3x-1,3x-1 - Simplify

Simplify expression - which expression is equivalent to: 3(m + 2) − 4(2m − 9) - Rectangular field

A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field.

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