# Examples for 8th grade - page 94

1. Paul earned Paul earned 300 Kč in one hour, Václav 1/3 more than Paul. Václav worked 60 hours, which is 1/3 fewer hours than Paul worked. How many percents less earned Paul an hour than Václav? How many hours did Paul more than Václav? How much did Paul earn more t
2. Summands Find two summands of the number 42, so that its product is minimized.
3. Square area Complete the table and then draw each square. Provide exact lengths. Describe any problems you have. Side Length Area . The angle of a straight road is approximately 12 degrees. Determine the percentage of this road.
5. Percents How many percents is 900 greater than the number 750?
6. Digit sum The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get the number 2430. What is the original two-digit number?
7. Surface area of the top A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder.
8. Percentages 5 \$5.25 is 7 1/2% of what number?
9. Inscribed sphere How many percents of the cube volume takes the sphere inscribed into it?
10. Two forces The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
11. Is right-angled Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 and √8) be a right triangle?
12. Windbreak A tree at a height of 3 meters broke in the windbreak. Its peak fell 4.5 m from the tree. How tall was the tree?
13. A square A square with length of diagonals 12cm give: a) Calculate the area of a square b) rhombus with the same area as the square, has one diagonal with length of 16 cm. Calculate the length of the other diagonal.
14. Scale factor A prism with a volume of 1458 mm3 is scaled down to a volume of 16mm3. What is the scale factor in fraction form?
15. Train delay The train should be in the station for 10 minutes. It still has 32 km left. What is the expected delay if the train travels in 2 minutes 3 km except for the last section where it is 2 km in 5 minutes.
16. Garden The garden around the new majer is divided as follows: 35% vegetable, 30% fruit orchards, 10% flowers and the remaining 120 m2 are lawns. What is the total area of the garden?
17. Diagonals at right angle In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD? Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters? Solve the following equation: 2x- (8x + 1) - (x + 2) / 5 = 9 The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced?