# Examples for 8th grade - page 16

- Square grid

Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm^{2}and circumference 12 cm and that their sides is in square grid. - n-gon

What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm? - Wood in the forest

The amount of wood in the forest was estimated at 7000 m^{3.}How much wood will be in forest after 2 years if the annual growth of wood is 2.2% each year and logging 70 m^{3}each year? - KLMN

In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN. - 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. - Triangular pyramid

Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm. - Barrel 3

Barrel with water has a weight 118 kg. When we get off 75% of water it has a weight 35 kg. How many kg has empty barrel? - Free fall

Lloyd fall from height 7 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s^{2} - Cylinder - h

Cylinder volume is 163 cm^{3.}Base radius is 10 cm. Calculate the height of the cylinder. - Height

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

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

How many possible ways are to shuffle 6 playing cards? - Lead cube

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

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

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