# Examples for 8th grade

1. Trapezoidal prism
Calculate the surface of the quadrilateral prism ABCDA'B'C'D 'with the trapezoidal base ABCD. The height of the prism is 12 cm; ABCD trapezoidal data: AB base length is 8 cm, CD base length is 3 cm, BC arm length is 4 cm, and AC diagonal length is 7 cm.
2. Krkonose CZ
Tourist's rod on the tourist route in the Krkonose was 1/5 of its length into the ground. Snow fell in winter and 1/3 of the length of the rod remained above the snow. Find the height of the snow if the length of the part above the snow is 32 cm greater
3. Cuboid - volume and areas
The cuboid has a volume of 250 cm3, a surface of 250 cm2 and one side 5 cm long. How do I calculate the remaining sides?
4. Similarity coefficient
The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ".
5. Mirror
How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m.
6. Cuboid walls
Calculate the volume of the cuboid if its different walls have area of 195cm², 135cm² and 117cm².
7. Cuboid height
What is the height of the cuboid if the edges of its base are 15 cm and 4 cm long and its volume is 420 cm cubic?
8. Average speed 4
Starting at home Tony traveled uphill to the store for 45 minutes at 8 miles per hour. he then traveled back home on the same path at a speed of 24 miles per hour. what is his average speed for the entire trip?
9. Rectangle 35
Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
10. Circle and rectangle
A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.
11. Three shapes
1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
12. Square
Danov's father has a square of 65.25 milligram square of wire with a diagonal. How will the square be big when one mm weighs 7 mg?
13. Trees - orchard
The 3/5 trees are apple trees and 1/3 of the trees are cherries. The remaining 5 trees are pear trees. How many trees are in the orchard.
14. Roses 2
Aunt Rose went to the flower shop to buy a bouquet with three roses. The flower shop had white, yellow and red roses. How many different flowers bouquet can a flower make for Aunt Rose create? Write all the bouquet options.
15. Triangular prism
Calculate the volume and surface of the triangular prism ABCDEF with base of a isosceles triangle. Base's height is 16 cm, leg 10 cm, base height vc = 6 cm. The prism height is 9 cm.
16. Crown coins
Jana saves two-crown and five-crown coins. She has ten coins in the cashier. How many two crowns and how many five crowns shw have if she saved 29 crowns?
17. Satin
Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?
18. Rhombus EFGH
Construct the rhombus EFGH where e = 6.7cm, height to side h: vh = 5cm
19. Metal pyramid
Find the weight of a regular quadrilateral pyramid with a 5 cm length and 6,5 cm body height is made from material with density g/cm3.
20. Fifth of the number
The fifth of the number is by 24 less than that number. What is the number?

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