# Units - math word problems

1. Cyclists Cyclist who rides at an average speed 16 km/h travels trip distance 10 min before the cyclist who rides at an average speed 11 km/h. What is the length of this cyclist trip(distance in km)?
2. Two balls Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
3. Hollow sphere Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
4. Trigonometry If you know that cos(γ) = sin (806°), what is the angle γ?
5. Magnification of the square If we increase the square side, increase the content of the 80 %. About what percentage was increased his sides?
6. Arm Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 14 cm and a height v=18 cm.
7. Scouts The boys from scout group traveled 5 days distance 115 km. Every day walked 1.5 km less than the previous day. How many kilometers scouts walked in the first day?
8. Tanker An oil tanker can be emptied by the first pump in 4.9 hours. Second pump can empty an tanker in 8 hours. If the first pump started at 4:00 and second 1.4 hour later, at what time will the tanker be empty?
9. Cone and the ratio Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
10. Sea on the Moon Assume that the Moon has sea, the same composition as on the Earth (has same density of salt water). Calculate dive of boat floating in the sea on the Moon, when on Earth has dive 3.6 m. Consider that the Moon has 6.5-times smaller gravitational accelerati
11. Train The train is running at speeds of 96 km/h. From the beginning of braking to full stop train run for 3.3 minutes. If the train slows the braking equally, calculate the distance of the place from the station where you need to start to brake.
12. Dog II Journey from a rangers' home to the town is 6 km. Mr. ranger started from his home and went 3 km per hour. His women came from the town and also went 3 km per hour. With ranger started dog and runs in 12 km in 1 hour. The dog went to ranger's women then.
13. Milk package Milk is sold in a box with dimensions of 9.5 cm; 16.5 cm and 6.5 cm. Determine the maximum amount of milk that can fit into a box. Coating thickness is negligible.
14. Triangle angles The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles.
15. Sector The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.
16. Block Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
17. Theatre Theatrical performance started at 15:50 and ended at 18:50. How many minutes long?
18. Vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
19. Truck Truck went for 4 hours and 30 minutes. If truck increase speed by 11 km/h, went same distance in 2 hours. Calculate this distance.
20. Mailbox Mailbox is opening at regular intervals 3 times a day. The first time is opened at 8:00 and the last at 19:00. Calculate hours when mailbox is opened during day.

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