# Examples for 8th grade - page 21

1. Circles Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square?
2. Right triangle Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
3. Family and age ratios Age of father and son are in the ratio 10:3; age of father and daughter are in the ratio 5:2. How old is father and son, if daughter is 20 years old? In what ratio is age sister and brother?
4. Tiles The room has dimensions 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover them room's floor.
5. Dog Man goes with a dog on a long walk 17 km from the house. Man is walking at speed 4.9 km/h and a dog that constantly running between house and man at 12.6 km/h. How many kilometers will run the dog when they reach their destination?
6. Insurance The owner of the house is insured against natural disasters and pays 0.04% annually of the value of house 77 Eur. Calculate the value of the house. Calculate the probability of disaster, if you know that 48% of the insurance is to pay damages.
7. Isosceles III The base of the isosceles triangle is 17 cm area 416 cm2. Calculate the perimeter of this triangle.
8. N-gon angles What is the sum of interior angles 8-gon? What is the internal angle of a regular convex 8-polygon?
9. Rectangle Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
10. Equilateral cylinder Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
11. Cuboid Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees).
12. Bits, bytes Calculate how many different numbers can be encoded in 16-bit binary word?
13. Children pool The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm. A) How many liters of water can fit into the pool? B) The pool is made of a double layer of plastic film.
14. Tetrahedral prism Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm. Convert magnitude of the angle α = 9°39'15" to radians:
16. Horizon The top of a lighthouse is 19 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.] Calculate the radius of the quadrant, which area is equal to area of circle with radius r = 15 cm.
18. Kids How many different ways can sit 8 boys and 3 girls in line, if girls want to sit on the edge?
19. Cone in cylinder The cylinder is inscribed cone. Determine the ratio of the volume of cone and cylinder. The ratio express as a decimal number and as percentage.
20. Perpendicular What is the slope of the perpendicular bisector of line segment AB if A[9,9] and B[9,-2]?

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