Examples for 9th grade - page 19
Find the cuboid that has the same surface area as the volume.
Man goes with a dog on a long walk 18 km from the house. Man is walking at speed 5.3 km/h and a dog that constantly running between house and man at 17.1 km/h. How many kilometers will run the dog when they reach their destination?
- Isosceles III
The base of the isosceles triangle is 24 cm area 416 cm2. Calculate the perimeter of this triangle.
- 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
Area of rectangle is 1430. Its length is 29 larger than the width. What are the dimensions of the rectangle?
- 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 3×?
- 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.
- Similarity n-gon
11-gones ABCDEFGHIJK and A'B'C'D'E'F'G'H'I'J'K' are similar. The area of 11-gon ABCDEFGHIJK is S1=254 cm2 and the diagonal length HG is 20 cm. Calculate area of the 11-gon A'B'C'D'E'F'G'H'I'J'K' if H'G' = 36 cm.
- Bits, bytes
Calculate how many different numbers can be encoded in 16-bit binary word?
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.]
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?
At party overyone clink with everyone. Together, they clink 406 times. How many people were at the party?
- 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.
- 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?
- 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.
Area of circle inscribed in a square is 6. What is the area of a circle circumscribed around a square?
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.
- Geometric mean
Calculate the geometric mean of numbers a=23.4 and b=16.8. Determine the mean by construction where a and b are the length of the lines.
- Triangle TBC
TBC is isosceles triangle with base TB with base angle 52° and legs length |TC| = |BC| = 30. How long is the base TB?