# Examples for 8th grade - page 14

1. 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 cm2 and circumference 12 cm and that their sides is in square grid.
2. 4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
3. 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.
4. 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.
5. 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°?
6. 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.
7. 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?
8. Trapezoid
Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
9. 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
10. Jewel
Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
11. 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
12. 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.
13. Sequence
In the arithmetic sequence is a1=-1, d=4. Which member is equal to the number 203?
14. Square
Calculate area of the square with diagonal 64 cm.
15. 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.
16. 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: ?
17. Circle and angle
What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
18. 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?
19. 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
20. Rhomboid
Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°.

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