# Expression of a variable from formula - problems - page 22

1. Cube diagonals The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
2. Nonagon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
3. Soldier An experienced soldier digs a good trench in 30 hours. Two soldiers dug the same trench each 40 hours. How many hours will the ditch dig all three together?
4. Pyramid cut We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm2. Find the area of the o
5. Car driver The car driver is in town A and is scheduled to be in town B at a specified hour. If it travels at an average speed of 50km/h, it will arrive in city B 30 minutes later. But if he travels at an average speed of 70km/h, he would arrive half an hour earlier
6. Peroxide How many ml 30% of peroxide (H2O2) should be poured into 100ml H2O to give a 20% solution?
7. Diagonals of a rhombus 2 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
8. Together 3 If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
9. The pole The telegraph pole is supported by a 4 m bullet at 3/4 of its height, the end of which is at a distance 2.5 m from the pole post. Calculate the height of the telegraph pole.
10. Tetrahedron What is the angle of the sides from the base of a three-sided pyramid where the sides are identical?
11. Orchard One-eighth of the trees in the fruit plant in winter froze and one-twelfth of damaged disease and pests. Healthy trees remained 152. Is it enough to supply 35 trees to restore the original number of trees in the orchard?
12. Sale discount The product was discounted so that eight products at a new price cost just as five products at an old price. How many percents is the new price lower than the old price?
13. Cube edges The sum of the lengths of the cube edges is 42 cm. Calculate the surface of the cube.
14. Cuboid The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.
15. Sugar production From 1 ton of beet, 150 kg of sugar is produced. To clean 1 ton of sugar 450 kg of lime is consumed. Calculate how many kgs of lime is consumed when processing 1 ton of sugar beet?
16. Two diggers Two diggers should dig a ditch. If each of them worked just one-third of the time that the other digger needs, they'd dig up a 13/18 ditch together. Find the ratio of the performance of this two diggers.
17. Bicycle gear The pedal bicycle wheel has 56 teeth and a rear 20 gear tooth. How many times does the bicycle wheel turn when you make 20 turns of the pedal wheel?
18. Cube edges If the edge length of the cube increases by 50%, how does the volume of this cube increase?
19. Body diagonal - cube Calculate the surface and cube volume with body diagonal 15 cm long.
20. Sum of squares The sum of squares above the sides of the rectangular triangle is 900 cm2. Calculate content of square over the triangle's hypotenuse.

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