# Problems for 8th grade

- Regular quadrangular pyramid

The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes? - The sides

The sides of a rectangle are in a ratio of 2:3, and its perimeter is 1 1/4 inches. What are the lengths of its side? Draw it. - A boy

A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff. - Diamond diagonals

Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm. - Shadow of tree

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? - Right angled triangle 3

Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees - Soaps

Each box has the same number of soaps. A quarter of all boxes contain only white soaps, and in each of the remaining 120 boxes there are always half the white soaps and half the green. White soaps total 1200. (a) the number of all soap boxes; (b) the sma - Two equations

Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5 - Three 43

Three brothers inherited a cash amount of 62,000 and they divided it among themselves in the ratio of 5:4:1. How much more is the largest share than the smallest share? - Surface area 6

Find the surface area of a prism whose bases are right triangles with sides of length 3, 4, and 5 inches and a height of 8 inches. Include a sketch - Water flow 2

How many litres of water will flow in 7 minutes from a cylindrical pipe 1 cm in diameter, if the water flows at a speed of 30 km per hour - Train speed

Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is: - Average age

The company of five people has an average age of 46 years. The average age of the first four is 43 years. How many years has the fifth member of this company? - Seven

Seven friends agree to send everyone a holiday card. How many postcards were sent? - A residential

A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, they constructed a water reservoir measuring 48m × 27m × 25m to collect the rain water. For how many days, the - Equilateral triangle

Calculate the area of an equilateral triangle with circumference 72cm. - 12 apples

12 apples and 2 loaves of bread cost 5.76 and 6 apples and 3 loaves of bread cost 7.68. How much is a loaf of bread? - 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? - Flying

The airplane from Prague to Bratislava was flying at a speed of 60 km/h less and back by 70 km/h greater than the original speed. What was the original speed if the plane returned to Prague according to the timetable? - Rhombus 29

One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus.

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