# Examples for 8th grade - page 14

- 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. - 4s pyramid

Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height? - 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. - 2x cone

Circular cone height 84 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone. - The chord

Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°? - Circle section

Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector. - Unknown x

If we add to unknown number 21, then divide by 6 and then subtract 51, we get back an unknown number. What is this unknown number? - Trapezoid

Are diagonals in a rectangular trapezoid perpendicular and bisect the angles? - Inheritance

After death father (♱ 62) remained mother (his wife) and its 3 children. Inheritance by law is that in first mother will automatically get half of the property and other one half inherite by heirs witch are mother and her 3 children by same share. Cal - Jewel

Rhombus-shaped jewel have area of 93 mm^{2}and the edge in long 13.2 mm. Calculate the size of rhombus acute angle. - Solidarity

Imagine a word solidarity means that salt donation to the needy, who have neither the salt. If we take word solidarity has word base salt + gift (only in Slovakian language). Calculate how many kilos of salt sympathetic citizen "gives" government a year i - Prism

The base of the prism is a rhombus with a side 30 cm and height 27 cm. The height of the prism is 180% longer than the side length of the rhombus. Calculate the volume of the prism. - Sequence

In the arithmetic sequence is a_{1}=-1, d=4. Which member is equal to the number 203? - Square

Calculate area of the square with diagonal 64 cm. - Pillar

Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48. - Stock market

Simon one day decided to invest € 62000 to the stock market. After six months he invested July 25 stock markets fell by 47%. Fortunately for Simon from July 25 5 to October 25 his shares have risen by 39%. Simon is then: ? - Circle and angle

What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad? - Painter Pavel

Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together? - Tea blend

Tea blends are maked from two kinds of tea. In standard tea mixture are two teas in the ratio 1:3 and 40 g costs 42 CZK. In the premium tea mixture are weighing two teas in the ratio 1:1 and 50 grams costs 60 CZK. How much cost 10 grams of more expensive k - Rhomboid

Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°.

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