# Examples for 9th grade - page 99

1. Hexagon ABCDEF
In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
2. 13 tickets
A short and long sightseeing tour is possible at the castle. Ticket for a short sightseeing circuit costs CZK 60, for a long touring circuit costs CZK 100. So far, 13 tickets have been sold for 1140 CZK. How much did you pay for tickets for a short tour?
3. The tourist
The tourist traveled 190km in 5 hours. Part of the journey passed at 5 km/h. The rest he went by bus at a speed of 60 km/h. How long has a bus gone?
4. Three sides
Side b is 2 cm longer than side c, side a is 9 cm shorter than side b. The triangle circumference is 40 cm. Find the length of sides a, b, c . .. .
5. Spruce height
How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
6. Distance of lines
Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm
7. Scientific notation
Approximately 7.5x105 gallons of water flow over a waterfall each second. There are 8.6x104 seconds in 1 day. Select the approximate number of gallons of water that flow over the waterfall in 1 day.
8. Lighthouse
Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea.
9. Bulb
A 60 W bulb consumes 0.12 kWh of electricity. How long did she stand light without a break?
10. Substitution
solve equations by substitution: x+y= 11 y=5x-25
11. Cutting square
From a square with a side of 30 cm, we cut the circle with the highest possible diameter. How many percents of the square content is this circle?
12. Car and motorcyclist
A car and a motorcyclist rode against each other from a distance of 190 km. The car drove 10km/h higher than the motorcyclist and started half an hour later. It met a motorcyclist in an hour and thirty minutes. Determine their speeds.
13. Two masters
The two masters will make as many parts as five apprentices at the same time. An eight-hour shift begins at 6 o'clock. When can a master finish the job to produce just as much as an apprentice for the whole shift?
14. Sss triangle
Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm
15. Stamps 2
Dennis spent 34.15 on stamps. The number of .56 is 10 less than four times of stamps bought for .41. How many of each stamp did he buy?
16. A box
A box is 15 centimeters long, 4 centimeters wide, and 3 centimeters tall what is the diagonal S of the bottom side? What is the length of the body diagnol R?
17. Height of the room
Given the floor area of a room as 24 feet by 48 feet and space diagonal of a room as 56 feet. Can you find the height of the room?
18. Diamond and diagonals
A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!)
19. Perimeter of RT
Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
20. Sphere floating
Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )

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