Examples for 9th grade - page 19
A force of 226 kg (2260 N) is required to pull a boat up a ramp inclined at 10° with horizontal. How much does the boat weight?
- Axial section
Axial section of the cylinder has a diagonal 18 cm. The size of the shell and the base surface are in the ratio 2:3. Calculate the volume and surface area of this cylinder.
- Triangle KLB
It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o
The top of a lighthouse is 12 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.]
- Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
Area of circle inscribed in a square is 6. What is the area of a circle circumscribed around a square?
- 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?
- 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.
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).
How many is subsets of set ??
Calculate height of the equilateral triangle if its perimeter is 54?
In how many points will intersect 11 different lines, where no two are parallel?
- 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.
Calculate distance between two points Z[7; -9] and U[-10; -8].
- ISO trapezium
Calculate area of isosceles trapezoid with base 53 long, leg 43 long and with the angle between the base and leg 70 degrees.
- Circumferential angle
Vertices of the triangle ΔABC lies on circle and divided it into arcs in the ratio 5:5:3. Determine the size of the angles of the triangle ΔABC.
Rectangular rink with dimensions of 79.5 m and 529 dm must be covered with a layer of ice 4.5 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 10.9% greater than the volume of water.
A school survey found that 9 out of 16 students like pizza. If 5 students are chosen at random, what is the probability that all 5 students like pizza?
In the middle of a cylindrical tank with a bottom diameter 350 cm is standing rod which is 31 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
Find the cuboid that has the same surface area as the volume.