# Examples for 9th grade - page 45

- Cube corners

From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body? - Sails

We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail? - Water in aquarium

The aquarium cuboid shape with a length of 25 cm and a width of 30 cm is 9 liters of water. Calculate the areas which are wetted with water. - Container with water

The weight of a container with water is 2.48 kg. If the cast 75% water, the container with water has a weight of 0.98 kg. Determine the weight of the empty container. How much water was originally in the container? - Medians in triangle

Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm. - Candies

In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ? - Chess

How many different ways can initiate a game of chess (first pass)? - Bathroom

How many CZK we pay for lining the perimeter walls of the bathroom with rectangular shape with dimensions 3.5 m and 4 m, high 1.5 m if 1 square m tile cost 300 CZK? - Right angled triangle 2

LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n - The city 2

Today lives 167000 citizens in city. How many citizens can we expect in 11 years if their annual increase is 1%? - Pumps

First pump flows 16 liters per second into the basin by the second pump 75% of the first and by third pump half more than the second. How long will take fill basin by all three pumps simultaneously volume 15 m^{3}(cubic meters)? - A three-digit numbers

Determine the total number of positive three-digit numbers that contain a digit 6. - Water reservoir

The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later than both together. For how long is filled by each separately? - Probabilities

If probabilities of A, B and A ∩ B are P (A) = 0.62 P (B) = 0.78 and P (A ∩ B) = 0.26 calculate the following probability (of union. intersect and opposite and its combinations): - Water

In the garden with an area of 8 ares rain 40hl of water. To what heights leveled water? - Direct route

From two different places A and B connected by a direct route, Adam (from city A) and Bohus (from city B) started at a constant speed. As Adam continued to go from A to B, Bohus turned around at the time of their meeting and at the same speed he returned t - Rings groups

27 pupils attend some group; dance group attends 14 pupils, 21 pupils sporty group and dramatic group 16 pupils. Dance and sporting attend 9 pupils, dance and drama 6 pupil, sporty and dramatic 11 pupils. How many pupils attend all three groups? - Harvesters

The first harvester reaps the grain from land for 24 hours, the second harvester for 16 hours. For how many hours will take harvest by two harvesters, but the second harvester started working four hours later than the first? - Center of gravity

In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT. - Znojmo

From Znojmo to Brno started truck with a trailer at an average speed 53 km per hour. Against him 14 minutes later from Brno started car with an average speed of 1.2-times greater than the truck. How long and how far from Znojmo, they meet if the distanc

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