# Examples for 9th grade - page 20

- Water container

Container with water weighs 1.48 kg. When we cast 75% of water container of water weight 0.73 kg. How heavy is an empty container? - Sphere growth

How many times grow volume of sphere if radius rises 5×? - Rectangle

Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle? - Axial section

Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder. - Triangular prism

Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume. - Similarity n-gon

9-gones ABCDEFGHI and A'B'C'D'E'F'G'H'I' are similar. The area of 9-gon ABCDEFGHI is S_{1}=190 dm^{2}and the diagonal length GD is 32 dm. Calculate area of the 9-gon A'B'C'D'E'F'G'H'I' if G'D' = 13 dm. - Bits, bytes

Calculate how many different numbers can be encoded in 16-bit binary word? - Cathethus and the inscribed circle

In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle. - Horizon

The top of a lighthouse is 17 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.] - Party

At party overyone clink with everyone. Together, they clink 171 times. How many people were at the party? - Boat

A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight? - Circles

Area of circle inscribed in a square is 14. What is the area of a circle circumscribed around a square? - Oil rig

Oil drilling rig is 23 meters height and fix the ropes which ends are 8 meters away from the foot of the tower. How long are these ropes? - Geometric mean

Calculate the geometric mean of numbers a=12.6 and b=26.8. Determine the mean by construction where a and b are the length of the lines. - Distance

Calculate distance between two points X[18; 19] and W[20; 3]. - Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees). - Two workers

Two workers together execute some work in 10 days. The first worker would have done himself in 20 days. How many days would have done himself a second worker? - Icerink

Rectangular rink with dimensions of 69.3 m and 567 dm must be covered with a layer of ice 2.9 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 10.2% greater than the volume of water. - Tetrahedral prism

Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm. - Circumferential angle

Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 5:3:10. Determine the size of the angles of the triangle ΔABC.

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