# Harder math problems - page 4 of 5

- Cone in cylinder

The cylinder is an inscribed cone. Find the ratio of the volume of the cone and cylinder. Please write the ratio as a decimal number and as a percentage. - One green

In the container are 45 white and 15 green balls. We randomly select five balls. What is the probability that there will be one green ball maximally? - House roof

The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How much m² is needed to cover the roof if the roof pitch is 57° and we calculate 11% of waste, connections, and overlapping of area roof? - Cube in a sphere

The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube.

- IS trapezoid

Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm. - Pizza

A school survey found that 10 out of 15 students like pizza. If 5 students are chosen randomly, what is the probability that all 5 students like pizza? - Climb

The road has climbing 1:27. How big is an angle correspond to this climbing? - Fertilizer

Mr. Gherkin uses for fertilization 10% solution of fertilizer. 5 liters of it still left. How much water must be added to the solution to make only the 7% solution? - Tanks

The fire tank has a cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used if the water level in the tank fell 5 cm? Wri

- Painting school

Redecoration school had scheduled for four crew to 10 days. After two days, a single worker was ill. For how many days was the school painted when remain workers working with the same tempo? - Rhomboid

Calculate the circumference and area of the rhomboid with sides 19 and 20, with their angle 40°. - Strawberries

Father collects strawberries himself in 4 hours, son in 14 hours. How long will it take them along when dad comes to help his son collect strawberries after 3 hours? - Euclid1

The right triangle ABC has hypotenuse c = 20 cm. How large sections cuts height h_{c}=9 cm on the hypotenuse c? - Vector sum

The magnitude of the vector u is 12 and the magnitude of the vector v is 8. The angle between vectors is 61°. What is the magnitude of the vector u + v?

- Clock

What time is now if the time elapsed afternoon is 2/10 of time that elapses before midnight? - Euclid3

Calculate the height and sides of the right triangle if one leg is a = 81 cm and the section of hypotenuse adjacent to the second leg c_{b}= 39 cm. - Insurance

The house owner is insured against natural disasters and pays 0.05% annually of the value of the house 88 Eur. Calculate the value of the house. Calculate the probability of disaster if you know that 50% of the insurance is to pay damages. - Two doctors

Doctor A will determine the correct diagnosis with a probability of 89% and doctor B with a probability of 75%. Calculate the probability of proper diagnosis if both doctors diagnose the patient. - Free fall

Pavel fall from height 9 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s²

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