# 6th grade (11y) + expression of a variable from formula - problems

1. Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
2. Theater
The theater has in each row with 19 seats. Ticket to the first 10 rows is for 30 USD. In next rows is for 15 USD. The theater was completely sold out. Revenue was 12255 USD. How many rows are in the theater?
3. Sea water
Mixing 34 kg of sea water with 34 kg rainwater is created water containing 3.4% salt. How many percent sea water contains salt?
4. Garden
Father dig up the garden in 9 hours. Son in 13 hours. How many hours take dig up the garden together?
5. Circle
How big is area of circle if its circumference is 80.6 cm?
6. Triangles
Equilateral triangle with side 40 cm has the same perimeter as an isosceles triangle with arm of 45 cm. Calculate the base x of an isosceles triangle.
7. Garden
Trapezoid garden has parallel sides 19 m and 24 m. Its area is 193.5 square meters. What is the width of the garden?
8. BMI index
Calculate BMI (body mass index, an index indicating obesity, overweight, normal weight, underweight) man weighing m = 71 kg and height h = 170 cm. Index is calculated according to equation (formula): ? With BMI index is possible to compare people of diff
9. Angles
The triangle is one outer angle 158°54' and one internal angle 148°. Calculate the other internal angles of a triangle.
10. Playground
Rectangular playground is fenced with 38 m long netting. Its width is 7 m. Calculate its length.
11. Flowerbed 2
Around the square flower bed in a park is sidewalk 2 m wide. The area of ​​this sidewalk is 243 m2. What is the area of the flowerbed?
12. Shape
Plane shape has a maximum area 677 mm2. Calculate its perimeter if perimeter is the smallest possible.
13. 7 triangle
The triangle area is 26.7 cm2. Determine the side length l if appropriate height hl = 45.3 cm.
14. Aquarium 6
How high is the water level in the aquarium with a rectangular base 40cm and 50cm if it is filled 0,65hl of water?
15. One and a half chicken
One and a half chicken bears one and a half egg in one and a half day. How many eggs can withstand from 6 chicken in 6 days?
16. Floor
Rectangular floor of living room has a length 5.4 meters and a circumference 17.2 meters. What is its width?
17. Third dimension
Calculate the third dimension of the cuboid: a) V = 224 m3, a = 7 m, b = 4 m b) V = 216 dm3, a = 9 dm, c = 4 dm
18. MO-Z5-3-66 tiles
The picture shows a square tiles with side 10 dm which is composed of four identical small rectangles and squares. Circumference of small square is five times smaller than the circumference of the entire tile. Determine the dimensions of the rectangle.
19. Cube 5
The content area of one cube wall is 32 square centimeters. Determine the length of its edges, its surface and volume.
20. Divide money 2
Ben and Dan had the same amount of money at the start. When Ben gave 300 to Dan, the ratio of Ben 's money to Dan's money became 2:3. How much money did each have at first?

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