# Examples for 9th grade - page 50

- Sphere cuts

At what distance from the center intersects sphere with radius R = 60 plane, if the cut area and area of the main sphere circle is in ratio 3/6. - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 236 dm. - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel. - Angles in triangle

The triangle is ratio of the angles α:β = 8:3. Angle γ is 40° greater than α. What are the size of angles of the triangle? - Profitable bank deposit 2012

Calculate the value of what money lose creditor with a deposit € 7700 for 4 years if the entire duration are interest 2.2% p.a. and tax on interest is 19% and annual inflation is 3.6% (Calculate what you will lose if you leave money lying idle at negative - Center of gravity

In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. - Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei - Way

If the current way to school was 2 km shorter then if Milan swipe one half he will have already one quarter of the way to school behind. How long is Milan's way to school? - Diagonals of a rhombus

One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus. - Two cyclists

Two cyclists started from crossing in the same time. One goes to the north speed 20 km/h, the second eastward at speed 26 km/h. What will be the direct distance cycling 30 minutes from the start? - Doubling

The message is spreading that each day has doubled the number of people who know about it. All know message for 20 days. How long known it eighth people? - One percent

One percent of all the lights in the city are LED, the remaining 99% are conventional. Other types are not there. John counted them honestly but he had counted only conventional. After a good dinner he registered numbers and he have notice that from all t - Baskets of apples

Grandfather gathered apples into baskets. He filled one large and three small baskets. Small baskets are identical and each can hold 3 kg of apples less than in a large basket. In small baskets together 3 kg of apples over a large basket. How many kilogram - Ravens

On two trees sitting 17 ravens. If 3 ravens flew from first to second tree and 5 ravens took off from second tree then the first tree has 2 times more ravens than second tree. How many ravens was originally on every tree? - Water wessel

The vessel containing water has a weight 19 kg. After pouring half the water its weigth 11 kg. What is the weight of the empty vessel? - Cycling trip

At 8 am started a group of children from the camp to day cycling trip. After 9:00 weather deteriorated sharply and the leader decided to send for the children bus on the same route, which started at 10 hours. For how long and at what distance from the camp - Price increase 2x

If two consecutive times we increase the price of the product by 20%, how many % is higher final price than the original? - Tetrahedral pyramid

It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges. - Euclid theorems

Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm. - The factory

The factory ordered 500 hexagonal steel bars of square section with 25 mm side. How many cars with a load capacity of 3 tonnes will be needed for bars move if the steel density is 7,850 kg.m-3?

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