# Examples for 9th grade - page 67

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. 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.
3. 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.
4. 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?
5. 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
6. 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?
7. 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?
8. 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.
9. Sum 10
What is the probability that two dice throw twice in a row will result the sum of 10?
10. Rectangle
The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
11. Rectangle - sides 4
Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.
12. 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.
13. Unknown number 10
Number first increased by 30%, then by 1/5. What percentage we've increased the original number?
14. Pet store
In a pet store, they are selling out the fish from one aquarium. Ondra wanted half of all fish, but they don't wish cut by hal fany fish he got one more than demanded. Matthew wished the remaining half of the fish, but as Andrew got half the fish more th
15. 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?
16. 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?
17. Steamer
At 6 hours 40 minutes steamer sailed from the port at speed 12 km/h. At exactly 10 hours started sail motorboat at speed 42 km/h. When motorboat will catch steamer?
18. 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?
19. Three ints
The sum of three consecutive integers is 2016. What numbers are they?
20. Hydrochloric acid
Determine the concentration of which must have a solution of hydrochloric acid that mixing 10 l of the solution with 8 liters of 26% solution to get the solution with a concentration of 50%?

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