# Grade - examples - page 196

1. Mixing water
The 30-liter container should we fill with water at 60 degrees Celsius. How many liters of water 80 degrees C hot and how many liters of water 20 degrees Celsius warm we have to mix?
2. The sides
The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it.
3. Volume of cone
Find the volume of a right circular cone-shaped building with a height of 9 cm and a radius base of 7 cm.
4. Grandmother
Mom walked out to visit her grandmother in a neighboring village 5km away and moved at a speed of 4km/h. An hour later, father drove down the same road at an average speed of 64km/h. 1) How long will take to catch mom die? 2) What is the approximate dis
5. Curved surface area CSA
A cylinder 5cm high has a base radius(7/2) cm. Calculate the curved surface area.
6. Prime number
Jan wrote any number from 1 to 20. What is the probability that he wrote the prime number?
7. Iceberg
What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
8. Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
9. Mixed2improper
Write the mixed number as an improper fraction. 166 2/3
10. Sum of fractions
What is the sum of 2/3+3/5?
11. KLMN trapezoid
The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K?
12. Rectangle diagonal
The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
13. Meat loses
Meat loses 18% of its weight by smoking. How much raw meat butcher used to manufacture 35 kilos of smoked?
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.
15. 3d printer
3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
16. Motorcyclist
From Trutnov, the motorcyclist started at an average speed of 60km/hour. At 12.30hrs the passenger car was started at a speed of 80km/hour. How many hours and at what distance from Trutnov will car catch a motorcycle?
17. Square root 2
If the square root of 3m2 +22 and -x = 0, and x=7, what is m?
18. Sugars
In what ratio must two sorts of sugar, costing #390 and #315 per kg respectively, be mixed in order to produce a mixture worth #369 per kg?
19. Sewing
Beth's mother can sew 235 pairs of short pants in 6 days while Lourdes can sew 187 pairs in 8 days. How many more pairs of short pants can Beth's mother sew?
20. Desks
A class has 20 students. The classroom consists of 20 desks, with 4 desks in each of 5 different rows. Amy, Bob, Chloe, and David are all friends, and would like to sit in the same row. How many possible seating arrangements are there such that Amy, Bob, C

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