# Expression of a variable from formula - problems - page 12

1. Hexagonal prism 2
The regular hexagonal prism has a surface of 140 cm2 and height of 5 cm. Calculate its volume.
2. Cuboid easy
The cuboid has the dimensions a = 12 cm, b = 9 cm, c = 36 cm. Calculate the length of the body diagonal of the cuboid.
3. Cruise liner
Cruise liner runs along the river between points A and B. The journey downstream takes 40 minutes 1 hour upriver. The flow rate of the river is 3 km/h. What is the speed of cruise liner?
4. Diagonals of diamond
Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
5. Cuboid edges in ratio
Cuboid edges lengths are in ratio 2:4:6. Calculate their lengths if you know that the cuboid volume is 24576 cm3.
6. Land - isosceles trapezoid
Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
7. Unknown number 5
Daniel think an integer. When he change this number at a ratio of 2:5 he got number 2.8. Determine what number think Daniel.
8. Tree
Between points A and B is 50m. From A we see a tree at an angle 18°. From point B we see the tree in three times bigger angle. How tall is a tree?
9. Church roof 2
The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m2 of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
10. Cuboid enlargement
By how many percent increases the volume of cuboid if its every dimension increases by 30%?
11. Cuboid surface
Determine surface area of cuboid if its volume is 52.8 cm cubic and length of the two edges are 2 cm and 6 cm.
12. Axial cut
The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
13. Family
Son is 3/5 smaller than the mother. Mother is 99 cm higher than the son. How tall is the mother?
14. Orchard
3/5 of the trees in the orchard are apples, 1/3 are cherries and the remaining five trees are pear. How many trees are in the orchard?
15. Apples 5
In six crates are 45 kg of apples. In five crates were the same amounth and in one crate was 3 kg of apples more. How many kg of apples were in each crate?
The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
17. Three children
3 children eat 8 chocolates in 6 days. How many chocolates 6 children eat in 18 days?
18. Cuboid
Cuboid has a surface of 516 cm2. Side a = 6 cm and b = 12 cm. How long is the side c =?
19. Midpoints
Triangle ABC with sides a = 5 cm, b = 3 cm, c = 40mm has a midpoint of K, L, M. How many centimeters is long perimeter of parallelogram KBLM?
20. Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.

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