# Harder math problems

- Toys

3 children pulled 6 different toys from a box. How many ways can toys be divided, so each child has at least one toy? - Pool

If water flows into the pool by two inlets, fill the whole for 19 hours. The first inlet filled the pool 5 hour longer than the second. How long does the pool take to fill with two inlets separately? - Rectangular cuboid

The rectangular cuboid has a surface area 5334 cm², and its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid. - Sphere

The sphere's surface is 12100 cm², and the weight is 136 kg. What is its density? - Axial section

The axial section of the cone is an equilateral triangle with an area 208 m². Calculate the volume of the cone. - Numbers

Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum? - Rectangle

In a rectangle with sides, 8 and 9 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than any side of the rectangle? - Tetrahedral pyramid

Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm, and the length of the edges of the base is 6 cm. - Pumps

The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump? - Crystal

The crystal grows every month 1.2 permille of its mass. How many months to develop a crystal from weight 177 g to 384 g? - Raffle

In the pool number from 1 to 115. What is the probability that a randomly selected number is not a prime number? - Triangle SAS

Calculate the triangle area and perimeter if the two sides are 105 dm and 68 dm long and angle them clamped is 50 °. - Rectangle - sides ratio

Calculate the area of a rectangle whose sides are in ratio 9:14 and perimeter is 388. - Workers

Two workers, A and B, will be done work together for 15 days. They worked together for 13.5 days. Then A worker became ill, and worker B finished the job alone for 7.5 days. If every worker was working alone, how many days took the whole work for workers - Shooters

In the army, regiments are six shooters. The first shooter target hit with a probability of 49%, next with 75%, 41%, 20%, 34%, 63%. Calculate the probability of target hit when shooting all at once. - TV fail

The TV has average 35 failures after 10,000 hours. Find the probability of TV failure after 400 hours of operation. - Mast

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast if the sun above the horizon is at an angle 45°12'. - 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. - Sales

From statistics of sales goods, item A buys 51% of people, and item B buys 59% of people. What is the probability that from 10 people buy 2 item A and 8 item B? - Cylinder - basics

Cylinder with base radius r = 54 cm and height h=35 cm. Calculate: a) Area of the base

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