Examples for 9th grade

Hexagon ABCDEF
In the regular hexagon ABCDEF, the diagonal AE has a length 8cm. Calculate the circumference and the hexagon area.
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.
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?
A cylinder
A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
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.
Two equations
Solve equations (use adding and subtracting of linear equations): -4x+11y=5 6x-11y=-5
Right angled triangle 3
Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length.
Diamond diagonals
Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm.
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 sm
Cube cut
The cube ABCDA'B'C'D ' has an edge of 12cm. Calculate the area of diagonal cut B DD'B '.
Divide
Divide area of rectangles with dimensions 32m and 10m by the ratio 7: 9. What area corresponds to a smaller section?
Body diagonal - cube
Calculate the surface and cube volume with body diagonal 15 cm long.
Roof cover
Above the pavilion with a square ground plan with a side length of a = 12 m is a pyramid-shaped roof with a height v = 4.5 m. Calculate how much m² of sheet metal is needed to cover this roof if 5.5% of the sheet we must add for joints and waste.
The room
The room has a cuboid shape with dimensions: length 50m and width 60dm and height 300cm. Calculate how much this room will cost paint (floor is not painted) if the window and door area is 15% of the total area and 1m2 cost 15 euro.
A bridge
A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water.
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:
Two melons
There are 2 melons in the box. Together they weigh 11kg. The weight of green is 3 kg less than three times the weight of yellow. What is the weight of a green melon?
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?
Rain
It rains at night. On 1 m² of lake will drop 60 liters of water. How many cm will the lake level rise?
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?

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