# Expression of a variable from formula - examples - page 15

1. Rectangle
The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm.
2. Body diagonal
The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
3. VAT on books
The cost of a book in the store is 12.5 euros. How much euros is the VAT of this book? VAT is 10%.
4. Trench
The trench is a four-sided prism. The cross section has a trapezoidal shape with basements of 4m and 6m, the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil.
5. Variance and average
Of the 40 values were calculated average mx = 7.5 and variance sx = 2.25. After the control was found to lack the two items of the values of x41 = 3.8 and x42=7. Correct the above characteristics (mx and sx).
6. Workers
9 workers dig a canal 120 meters long for eight hours. For how long would be dig five workers canal 200 meters long?
7. Chocolate roll
The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this.
8. Contract
8 employees complete the contract for 65 hours. After 17 hours, 3 employees had to leave for another job. How many more hours will the job on contract be fulfilled?
9. Price saleoff
Shoes standing y euros. At first they were discounted by 12% and then 50% of the new amount. After this double cheapening the cost was exactly 22 euros. Determine the original price of shoes.
10. Unknown number
Determine the unknown number, which double of its fourth square is equal the fifth its square.
11. Vacation
Tomas spent 60% of his savings for his weekly vacation. He was 32 € left. How many euros did he have before vacation?
12. Wall diagonal
Calculate the length of wall diagonal of the cube whose surface is 384 cm square.
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =?
14. Square s3
Calculate the diagonal of the square, where its area is 0.49 cm square. And also calculate its circumference.
15. The cylinder base
The cylinder with a base of 8 dm2 has a volume of 120 liters. From a cylinder fully filled with water, 40 liters of water was removed. At what height from the bottom /with precision to dm/ is the water level?
16. Cows
Agricultural cooperative has increased the number of housed cows by 14% to 285 units. By how many cows increased agricultural cooperative the number of cows?
17. Cube walls
Find the volume and surface area of the cube if the area of one wall is 40cm2.
18. Wine
A bottle of wine costs 21 euros; and wine is 20 times more expensive than a bottle. How much a bottle cost?
19. Trucks
Three lorries droved bricks. One drove n bricks at once, second m less bricks than the first and third 300 bricks more the first lorry. The first lorry went 4 times a day the largest went 3 times a day and the smallest 5 times a day. How many bricks br
20. Tank diameter
A cylindrical tank has a volume of 60 hectoliters and is 2.5 meters deep. Calculate the tank diameter.

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