# Harder math problems - page 2 of 5

- Event probability

The probability of event $J in $n independent experiments is $p. What is the probability that the event $J occurs in one experiment (chance is the same)? - Cylinder - basics

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

A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - Rectangle - sides ratio

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

- Pairs

At the table sit 10 people, 5 on one side and 5 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit? - Bridge

The bridge arc has a span of 159 m and height 14 m. Calculate the radius of the circle arc of this bridge. - Interested 7090

We call a natural number N bombastic if it contains no zero in its notation and if no smaller natural number has the same product of digits as the number N. Charles first became interested in bombastic prime numbers and claimed that there were not many of - 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. - R Trapezium

Rectangular trapezium has bases 21 and 10 and area 92 cm². What is its perimeter?

- Components

The 8 white, 4 blue, and 2 red components are in the box. What is the probability that we pull one white, one blue, and one red component without returning it? - Dices throws

What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once - Circle arc

The circle segment has a circumference of 135.26 dm and 2096.58 dm² area. Calculate the radius of the circle and the size of the central angle. - Cylinders

The area of the side of two cylinders is the same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume, and by how much? - Hands

The clock shows 12 hours. After how many minutes will the angle be between the hour and minute hand 90°? Consider the continuous movement of both hands for hours.

- Tower

The top of the tower is a regular hexagonal pyramid with a base edge 6.1 meters long and a height 11.7 meters. How many m² of the sheet is required to cover the top of the tower? We must add 9% of metal for waste. - Sphere fall

How much percent fall volume of a sphere if diameter decreases 3×? - Family

What is the probability that a family with 3 children has: exactly 1 girl? 2 girls and 1 boys? Consider the birth probability of a girl is 48.66% and a boy 51.34%. - Liters in cylinder

Determine the height at which level 24 liters of water in a cylindrical container having a bottom diameter 36 cm. - Peroxide

How much-distilled water (in liters) must pharmacists pour into 300 ml of 23.6% solution of hydrogen peroxide to get 2.7% solution to gargle?

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