# Examples for 8th grade - page 20

1. Inscribed rectangle The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
2. Trapezoid MO-5-Z8 ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
3. Triangular prism Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
4. Map Forest has an area of ​​36 ha. How much area is occupied by forest on the map at scale 1:500?
5. Rectangle diagonals It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
6. Root Use law of square roots roots: ?
7. Shots 5500 lead shots with diameter 4 mm is decanted into a ball. What is it diameter?
8. Sales vs profit Apple sells 22 percent less computes than the Acer but the profit from their sales is 2.2 times higher than Acer. How many times are Apple computer more expensive than Acer?
9. Circumferential angle Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 2:2:9. Determine the size of the angles of the triangle ΔABC.
10. Father and son Father is three times older than his son. 12 years ago father was nine times older than the son. How old are father and son?
11. Euler problem Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels?
12. Felix Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
13. Two workers Two workers together execute some work in 10 days. The first worker would have done himself in 20 days. How many days would have done himself a second worker?
14. Count of roots How many solutions has equation x. y = 7757 with two unknowns on the set of natural numbers?
15. Water container Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container?
16. Sphere growth How many times grow volume of sphere if diameter rises 10×?
17. Segments Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
18. Intersections How many intersections have circles with radius 16 mm and 15 mm, if the distance of their centers is 16 mm.
19. 9.A 9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5?
20. Pizza A school survey found that 12 out of 15 students like pizza. If 6 students are chosen at random, what is the probability that all 6 students like pizza?

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