Examples for 9th grade - page 48
- Cube from sphere
What largest surface area (in cm2) can have a cube that was cut out of a sphere with radius 22 cm?
- Two months
Mars has two months, Phobos and Deimos. Phobos orbits around Mars in 7 hours 39 minutes and Deimos in 30 h 14 min. How long will repeat the relative position of the three celestial bodies?
- Interest p.a.
Calculate the value of interest in period of 1 year from the deposit 62000 CZK at 8 percent interest rate, after deducting 15 percent tax.
- Chocholate pyramid
How many chocolates are in the third shelf when at the 8th shelf are 41 chocolates in any other shelf is 7 chocolates more the previous shelf.
- Rotating cone
Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
- Obtuse angle
The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)
- Cars speeds
Distance from city A to city B is 108 km. Two cars were simultaneously started from both places. The speed of a car coming from city A was 2 km/h higher than the second car. What was the speed of each car if they met in 54 minutes?
- Three men
Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old?
- Ratio of two unknown numbers
Two numbers are given. Their sum is 30. We calculate one-sixth of a larger number and add to both numbers. So we get new numbers whose ratio is 5:7. Which two numbers were given?
What amount of 80% solution and what amount of water is needed to mix in order to obtain two liters of 60% solution of this mixture?
- Cuboid - volume and areas
The cuboid has a volume of 250 cm3, a surface of 250 cm2 and one side 5 cm long. How do I calculate the remaining sides?
arc length = 17 cm area of sector = 55 cm2 arc angle = ? the radius of the sector = ?
Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm.
Blade circular saw with a diameter 42 cm turns 825 times per minute. Expresses his cutting speed in meters per minute.
- Alfa, beta, gama
In the triangle ABC is the size of the internal angle BETA 8 degrees larger than the size of the internal angle ALFA and size of the internal angle GAMA is twice the size of the angle BETA. Determine the size of the interior angles of the triangle ABC.
- Fifth of the number
The fifth of the number is by 24 less than that number. What is the number?
Weight of cargo car is 761 kg. Weight of car is 23% of the total weight of car+cargo. What is the weight of the cargo load?
Calculate the area of what may vary rectangular, if it focused by surveyor and found the dimensions 14 x 12 m while in each of the four joint points can be position deviation 8 cm?
How many real roots has equation ? ?
The first Earth satellite was flying at speed 8000 m/s. At that rate he circled the earth in 82 minutes. Jet flies at an average speed 800 km/h. How long would it take circle the earth round?