9th grade (14y) + expression of a variable from formula - examples - page 9

1. 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.
2. 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?
3. Diagonals of diamond Find the area and circumference of the diamond ABCD with 15m and 11m diagonals.
4. 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.
5. 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?
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. 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?
8. Cuboid enlargement By how many percent increases the volume of cuboid if its every dimension increases by 30%?
9. Axial cut The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume. The ladder is 10 m long The ladder is 8 m high How many meters is the distant heel from the wall?
11. Three children 3 children eat 8 chocolates in 6 days. How many chocolates 6 children eat in 18 days?
12. Wall height Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm.
13. 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?
14. Chairs Determine the number of seats in the seventh row and ninth row, if 3rd row has 14 seats and in every next row of seats has five more than the previous row.
15. Truncated cone 3 The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang.
16. Circle's chords In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.
17. Apples 2 Dried apples contain 15% water. Fresh apples contain 80% water. How many kg of apples we need buy in order to get 3 kg of dried apples?
18. Diagonals of a rhombus One of the diagonals of a rhombus is twice as the other. If the sum of the lengths of the diagonals is 24, find the area of the rhombus.
19. Four integers Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
20. The swing To swing the two girls. Aneta weight 45 kg and Simon 35 kg weight. How far should sit Simon from the middle of swing so it is balanced, if we know that Aneta is sitting at distance 1,5m? How far are girls sitting apart?

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