# Examples for 9th grade - page 38

- Three numbers

The sum of the three numbers is 287. These numbers are in a ratio of 3: 7: 1/4 Define these numbers - Two boxes-cubes

Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge? - 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. - Three-digit numbers

How many three-digit numbers are from the numbers 0 2 4 6 8 (with/without repetition)? - Medal

Calculate the approximate weight of the gold Olympics medal, if its diameter is 8 cm and a thickness 6 mm. The density of gold find out in the tables or on the Internet. - Cylinder

The cylinder surface is 859 dm^{2}, its height is equal to the radius of the base. Calculate height of this cylinder. - Nuts, girl and boys

Milena collected fallen nuts and called a bunch of boys let them share. She took a condition: the first boy takes one nut and tenth of the rest, the second takes 2 nuts and tenth new rest, the third takes 3 nuts and tenth new rest and so on. Thus managed. - Parallelogram +ľ

| AB | = 76cm, | BC | = 44cm, angle BAD = 30 °. Find the area of the parallelogram. - Cars

Cars started at 7:00 AM. From point A car run at 40 km per hour, from B car run 70 km per hour. Between A and B is 250 km long road. When and where will meet (measured from point A)? - Motion 2

At 10 o'clock started from place A car speed at 90 km/h. 20 minutes after started from the place B at speed 60 km/h another car. Distance places A and B is 120 kilometers. What time and where they meet? - Freight and passenger car

The truck starts at 8 pm at 30 km/h. Passenger car starts at 8 pm at 40 km/h. Passenger arrives in the destination city 1 hour and 45 min earlier. What is the distance between the city of departure and destination city? - Digging companies

Company A would dig a pit for 12 days, company B for 15 days, company C for 20 days and the company D for 24 days. Work began together companies C and D, but after three days joined them other two companies. How long took to dig a pit? - Arc

What area of a circle occupied the flowers planted in the arc of a circle with radius 4 m with central angle 45°? - Square Number

If to a square of integer number add 31, we get the square of next integer number. What is the original number? - Round table

Round table with diameter d = 105 cm is coated by square tablecloth with a side length 121 cm. About how many cm is higher center of tablecloth than its cornes? - 3d vector component

The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3? - Golden ratio

Divide line of length 14 cm into two sections that the ratio of shorter to greater is same as ratio of greater section to whole length of the line. - Nuts

How many we must have at least nuts if we can equally divide it to 10 children, 11 children or 19 children and any nut left? - Mr Novak

Mr Novak earns an average 1249 euros. When increasing the salary they gave him a choice: ? What is better choice for Mr Novak? - Cups

We have three cups. In the cups we had fluid and boredom we started to shed. 1 We shed one-third of the fluid from the second glass into the first and third. 2 Then we shed one quarter cup of liquid from the first to the second and to the third. 3 Then

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