# Examples for 9th grade - page 66

1. Four sided prism Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
2. Cablecar Funicular on Petrin (Prague) was 408 meters long and overcomes the difference 106 meters in altitude. Calculate the angle of climb.
3. Painter How many euros we will pay for repainting the room shaped cuboid with a length of 4.5 meters, width of 2.5 meters and a height of 3 meters, if for 1 m2 with paint we pay € 1.5?
4. Dining room The dining room has 11 tables (six and eight seats). In total there are 78 seats in the dining room. How many are six-and eight-seat tables?
5. Divisibility Write all the integers x divisible by seven and eight at the same time for which the following applies: 100
6. Candies If Alena give Lenka 3 candy will still have 1 more candy. If Lenka give Alena 1 candy Alena will hame twice more than Lenka. How many candies have each of them?
7. Sum 10 What is the probability that two dice throw twice in a row will result the sum of 10?
8. Three friends Three friends divided the profit 104,650 CZK, so that for every 4 CZK, which got the first friend equals 5 crowns for second and for every 9 CZK, which got the second equals 16 CZK for third. Question: Who got the most and how much.
9. Positive number z Positive number z is 10% greater than the number y. How many % is y smaller than z? Report the result rounded to one decimal place.
10. Mom and daughter Mother is 39 years old. Her daughter is 15 years. For many years will mother be four times older than the daughter?
11. Water tank The water tank has a cylindrical shape with a base diameter of 4.2 m and is 80 cm deep. How many minutes will take fill it 10 cm below the edge of the tank if water flowing 2 liters per second?
12. Costume Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand De
13. Mirror How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m.
14. Collecting For the first week of material collection events are picked up at the school 850 kg of paper and 305 kg of rags which represented 55% of total collection for 14 days. How many kilograms of secondary raw materials were handed over totally?
15. Store Peter paid in store 3 euros more than half the amount that was on arrival to the store. When he leave shop he left 10 euros. How many euros he had upon arrival to the store?
16. Rectangle The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
17. Right triangle eq2 Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
18. 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?
19. Sweets We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How much of this two types of candy is necessary to prepare this mixture?
20. Rectangle - sides 4 Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.

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