# Expression of a variable from formula - examples - page 16

1. Cube 1-2-3 Calculate the volume and surface area of the cube ABCDEFGH if: a) /AB/ = 4 cm b) perimeter of wall ABCD is 22 cm c) the sum of the lengths of all edges of the cube is 30 cm.
2. Price increase A 20 percent price increase meant a 90-crown raise. How many cost a product after?
3. Cylindrical tank Cylindrical tank holds 600hl water and is deep 2.5 m. Calculate the diameter of the cylinder.
4. A mast A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken?
5. Rectangle Calculate area of the rectangle if its length is 12 cm longer than its width and length is equal to the square of its width.
6. Cargo Car with cargo weight 7610 kg. Weight of car is 23% of the total weight of car and cargo. How heavy is cargo?
7. Rectangular triangle PQR In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal
8. Diagonal of square Calculate the side of a square when its diagonal is 10 cm.
9. Determine AP Determine the difference of the arithmetic progression if a3 = 7, and a4 + a5 = 71
10. Geometric seq Find the third member of geometric progression if a1 + a2 = 36 and a1 + a3 = 90. Calculate its quotient.
11. Diagonals Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.
12. Red balls In the bag there are 3 red, 12 blue and 8 green balls. How many red balls we must be attached to the bag if we want the probability of pulling out the red balls was 20%?
13. Two machines Performances of two machines are in a ratio of 7:12. A machine with less power produced 406 pieces of products per shift. a) How many pieces produced per shift second machine? b) How many pieces produced two machines together for five shifts?
14. Quotient Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4.
15. Coach Average age of 24 players and a coach of one team is 24 years. The average age of players without a coach is 23 years. How old is the coach?
16. Equilateral triangle ABC In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle conta
17. Hotel The hotel has a p floors each floor has i rooms from which the third are single and the others are double. Represents the number of beds in hotel.
18. Chord It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
19. The gardener The gardener bought trees for 960 CZK. If every tree were cheaper by 12 CZK, he would have gotten four more trees for the same money. How many trees did he buy?
20. Q of GP Calculate quotient of geometric progression if a1=5 a a1+a2=12.

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