# Examples for 8th grade - page 16

- n-gon

What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm? - Reservoir + water

Reservoir completely filled with water weighs 12 kg. After pouring off three quarters of the amount of water weights 3 kg. Calculate the weight and volume of the reservoir. - Playing cards

How many possible ways are to shuffle 7 playing cards? - Height

Is right that in any right triangle height is less or equal half of the hypotenuse? - Cylinder - h

Cylinder volume is 215 cm^{3}. Base radius is 2 cm. Calculate the height of the cylinder. - Hexagon - MO

The picture shows the ABCD square, the EFGD square and the HIJD rectangle. Points J and G lie on the side CD and is true |DJ| - Right triangle

Calculate the missing side b and interior angles, perimeter and area of a right triangle if a=10 cm and hypotenuse c = 16 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? - Lead cube

Calculate the edge of the cube made from lead, which weighs 19 kg. The density of lead is 11341 kg/m^{3}. - Rhombus

Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus? - 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 - 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? - 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. - 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? - Wire D

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

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

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