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×?
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 S1=190 dm2 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.
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.]
At party overyone clink with everyone. Together, they clink 171 times. How many people were at the party?
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?
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.
Calculate distance between two points X[18; 19] and W[20; 3].
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?
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.