# Examples for 8th grade - page 92

1. Hexagon cut pyramid Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
2. Three painters The three painters have painted bridge. The first would work done in 5 days, the second in 6 days, and the third in 7.5 days. How long will the bridge work if they work together?
3. Pumps After the floods, four equally powerful pumps exhausted water from the flooded cellar in 6 hours. How many hours would take a drained out with three equally powerful pumps?
4. Magic number The number 135 split to two addends so that one addend was 30 greater than 2/5 the addend.
5. Iron collecting Class 7A collected 3.2 tonnes of iron more than class 7B. Together they collected 6.4 tonnes of iron to the secondary raw material collection. How much did each class collect?
6. Surface of cubes Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each part made a cube. In what ratio are the surfaces of these cubes?
7. Area of iso-trap Find the area of an isosceles trapezoid, if the lengths of its bases are 16 cm, and 30 cm, and the diagonals are perpendicular to each other.
8. Diagonals A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal.
9. Diagonal he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
10. Points on line segment Points P & Q belong to segment AB. If AB=a, AP = 2PQ = 2QB, find the distance: between point A and the midpoint of the segment QB.
11. Remainder A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?
12. Mushrooms Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?
13. Trapezoid - intersection of diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.
14. Embankment Perpendicular cross-section of the embankment around the lake has the shape of an isosceles trapezoid. Calculate the perpendicular cross-section, where bank is 4 m high the upper width is 7 m and the legs are 10 m long.
15. Unknown number 17 Milada said, I am thinking of a number such that I evaluate expression x1/3, the value of the expression would be 5. Which number Milada thinking?
16. Candy Peter had a sachet of candy. He wanted to share with his friends. If he gave them 30 candies, he would have 62 candies. If he gave them 40 candies, he would miss 8 candies. How many friends did Peter have?
17. How far From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
18. Unknown numbers The sum of two consecutive natural numbers and their triple is 92. Find these numbers.
19. Clubhouse There were only chairs and table in the clubhouse. Each chair had four legs, and the table was triple. Scouts came to the clubhouse. Everyone sat on their chair, two chairs were left unoccupied, and the number of legs in the room was 101. How many chairs w
20. Rhombus construction Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...

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