# Examples for 9th grade - page 16

- Truncated cone

Calculate the height of the rotating truncated cone with volume V = 1057 cm^{3}and a base radii r_{1}= 8.1 cm and r_{2}= 9.7 cm. - 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? - Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm. - 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? - 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 - 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)? - Pairs

At the table sit 8 people, 4 on one side and 4 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit? - 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 cm^{2}. - 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? - 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? - House roof

The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m^{2}is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof? - Rotating cone II

Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm. - Wire D

Wire length 1 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle. - V-belt

Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm. - Triangle in circle

Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC. - 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)? - Arm

Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 18 cm and a height v=17 cm. - Trigonometry

If you know that cos(γ) = sin (806°), what is the angle γ? - 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 cm^{2}. What is the area of the trapezoid? - Scrap

From 6 products are 3 scrap. What is the probability that the random pick of 2 products have no defective product?

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