# Grade - examples - page 26

1. Sphere in cone
A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
2. Moving
Vojta left the house at three o'clockat 4 km/h. After half hour later went from the same place Filip by bicycle at speed 18 km/h. How long take Tilip to catch up Vojta and how far from the house?
3. Rhombus
Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus?
4. Children in the classroom
How many children are in the classroom, where Ladislav is 10th lightest and 16th heaviest in class?
5. Camp
In a class are 26 children. During the holidays 16 children were in the camps and 14 children on holiday with their parents. Determine the minimum and maximum number of children that may have been in the camp and on holiday with their parents at the same
6. MO - triangles
On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB se
7. Scrap
From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?
8. Water inlets
Inlet valve with a flow rate of 12 liters per second is filled tank for 72 minutes. How long take to fill full tank if we open one more such valve half an hour after?
9. Train
A passenger train traveled for 2 hours 74 km. 3.1 hours after its departure started fast train and caught it on 186 km. How many km/h is different its average speeds?
An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 44.1°W. How far is the plane from the airport (round to the nearest mile)?
11. Track arc
Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)?
12. Sales
From statistics of sales goods, item A buy 51% of people and item B buys 59% of people. What is the probability that from 10 people buy 2 item A and 8 item B?
13. Father and son
Father and son are together 80 years. Son is 28 years younger than father. How old is the son?
14. Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
15. Carpet
The room has rectangle shape with dimensions 4 m × 3.8 m. How many meters of carpet a width of 3 need to buy to cover the entire room?
16. Rotating cone II
Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
17. Prism
The lenght, width and height of a right prism are 6, 17 and 10 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?
18. Division
Three siblings Helena, Oliver and George split the bag with candies on merit in the ratio 6:1:4. How many candies should each get if in bag were 88?
19. House roof
The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
20. Trapezoid - diagonal
Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?

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