# Examples for 9th grade - page 48

- Pyramid in cube

In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid. - Perimeter of circle

Calculate the circumference of described circle to the triangle with sides 9,12,15 cm. - Sprinter

Sprinter runs the relay 4 x 400 m to the handover at speed 42 km/h. A second runner is at the start of the handover area 20 m long and runs when it is the first sprinter at distance 10 m. Calculate the speed at which the second runner must run in order to. - Profits

Two members will make profit 52 000, - EUR. The forst earned 8% more and the second 10% more and thus earned together 56 700, - EUR. How many will initially each earn? - Stock

Enterprise sold 7/12 of their products to foreign markets and 2/5 of the remainder sold at home. How many % of the products is still in stock? - Right angled triangle 2

LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n - Cuboid - volume and areas

The cuboid has a volume of 250 cm^{3,}a surface of 250 cm^{2}and one side 5 cm long. How do I calculate the remaining sides? - Ring

The ring made from gold and copper alloy has a weight of 14.5 g and a volume of 1.03 cm^{3.}How much gold and how much copper it contains? The metal densities are Au 19.3 g/cm³ and Cu 8.94 kg·dm-3 - Two pipes

One pipe fill one-fifth volume 20 minutes before by second one. The two pipes together will fill the tank in two hours. How long is will fill tank each pipe separately? - Scouts

Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type? - Legs

In the room are four-legged chairs, three-legged stool, and all are sitted with (one) people. I counted all the leg room and there were a total of 39. How many are there chairs, stool and people? - Eva

When Eva buys 8 packages of cookies 4 CZK left her. If she wanted to buy 10 packages, she would have to borrow 20 CZK. How much money has Eva in her wallet? - Parachutists

Parachutists during freefall firstly held in groups of 4, then of 6, then 9, 12 and finally of 18 members. How many parachutists jump at least should be, if at each group must all be involved. - Rhombus A2p

Rhombus area is 13 cm^{2}and its height is 5cm long . Determine a perimeter of this rhombus. - Three workers

Three workers were rewarded CZK 7200 and the money divided by the work they have done. First worker to get twice than the second, the second three times more than the third. How much money each worker received? - MATES

In MATES (Small Television tipping) from 35 randomly numbers drawn 5 winning numbers. How many possible combinations there is? - 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. - Cube from sphere

What largest surface area (in cm^{2}) can have a cube that was cut out of a sphere with radius 22 cm? - Two trains meet

From A started at 7:15 express train at speed 85 km/h to B. From B started passenger train at 8:30 in the direction to A and at speed 55 km/h. The distance A and B is 386 1/4 km. At what time and at what distance from B the two trains meet? - 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?

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