# The most difficult problems

#### Number of problems found: 6626

• 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.
• Ratio of sides
Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
• 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?
• Big family
A certain number of people met at the family celebration - their average age was three times the number present. Then came my grandfather, who was 75 years old and the average age was again three times the number present. How many people are celebrating r
• 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
• 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?
• Profit growth
The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods?
• Athletic competition
In a 400 meter athletic competition, a participant covers the distance as given below. find the average speed? first 80 meters 10 m/s next 240 meters 7.5 m/s last 80 meters 10 m/s
• 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?
• Mixing Celsius and Fahrenheit
Add up three temperatures: 5°F +6°F +0°C
• 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)
• 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.
• Find the sum
Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5
• 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?

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