# Examples for 9th grade - page 44

- Algebrogram

Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI - Rectangular trapezoid

Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC. - Pyramid in cube

In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid. - Miraculous tree

Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 6 days? - Car

At what horizontal distance reaches the car weight m = 753 kg speed v = 74 km/h when the car engine develops a tensile force F = 3061 N. (Neglect resistance of the environment.) - Wheels

Small tractor wheel with a diameter of 60 cm must be rotated 8 times to overcome some pathway. How many times must turn the big tractor wheel with a radius 60 cm to overcome the same distance? - Five tractors

Five tractors plow field in 4.8 hours. How long plow this field if after 1.5 hours of work two tractors went to a different field? - Candies

In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ? - Cuboid - volume and areas

The cuboid has a volume of 250 cm^{3}, a surface of 250 cm^{2}and one side 5 cm long. How do I calculate the remaining sides? - Barrel 2

Empty barrel weighs 7 kg. When it filled with water up to 45% height, weighs 60 kg. How heavy is barrel full of water? - Rectangle Anton

Difference between length and width of the rectangle is 8. Length is 3-times larger than the width. Calculate the dimensions of the rectangle. - Parcel

Both dimensions of the rectangular parcel were increased by 26%. By how many % has increased its acreage? - Tractor wheels

Smaller tractor wheel has a circumference of 3 meters, bigger 4 meters. On what path executes smaller wheel 6 turns over more bigger? - Water in aquarium

The aquarium cuboid shape with a length of 25 cm and a width of 30 cm is 9 liters of water. Calculate the areas which are wetted with water. - Silo

Outer perimeter of silo is 32 m. Concrete wall is 35 cm thick. What is diameter and area of inside floor of silo? - Medians in triangle

Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm. - Cube corners

From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body? - Right angled triangle 2

LMN is a right angled triangle with vertices at L(1,3), M(3,5) and N(6,n). Given angle LMN is 90° find n - Sails

We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail? - Container with water

The weight of a container with water is 2.48 kg. If the cast 75% water, the container with water has a weight of 0.98 kg. Determine the weight of the empty container. How much water was originally in the container?

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