# Examples for 9th grade - page 18

- Circumscribing

Determine the radius of the circumscribed circle to the right triangle with legs 3 cm and 3 cm. - Triangular prism

The base perpendicular triangular prism is a right triangle whose hypotenuse measures 13 cm and one cathetus 2 cm. Height of the prism is equal to 10/7 of the perimeter of the base. Calculate the surface area of prism. - Felix

Calculate how much land saw Felix Baumgartner after jump from 22 km above ground. The radius of the Earth is R = 6378 km. - Hollow sphere

Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m^{3} - Sphere growth

How many times grow volume of sphere if radius rises 3×? - Machine

Price of the new machine is € 56000. Every year is depreciated 16% of residual value. What will be the value of the machine after 5 years? - Rectangle

Area of rectangle is 1430. Its length is 29 larger than the width. What are the dimensions of the rectangle? - Sales vs profit

Apple sells 45 percent less computes than the Acer but the profit from their sales is 1.7 times higher than Acer. How many times are Apple computer more expensive than Acer? - Bits, bytes

Calculate how many different numbers can be encoded in 16-bit binary word? - Euler problem

Someone buys a 720 tolars towels. If it was for the same money of 6 more towels, it would be 6 tolars cheaper each. How many were towels? - MO - triangles

On the AB and AC sides of the triangle ABC lies successive points E and F, on segment EF lie point D. The EF and BC lines are parallel and is true this ratio FD:DE = AE:EB = 2:1. The area of ABC triangle is 27 hectares and line segments EF, AD, and DB se - 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? - Inscribed rectangle

The circle area is 184. Determine the area of inscribed rectangle with one side 10 long. - Triangle and its heights

Calculate the length of the sides of the triangle ABC, if v_{a}=13 cm, v_{b}=17 cm and side b is 5 cm shorter than side a. - 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 S_{1}=254 cm^{2}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. - Dog

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? - Boat

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? - Two balls

Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them. - Party

At party overyone clink with everyone. Together, they clink 406 times. How many people were at the party? - Workers

Workers digging a jump pit in the school yard. Pit has a cuboid shape with a length 20 m, a width 20 dm and depth 36 cm. They excavate 0.4 cubic meters of soil an hour. How much time (hours and minutes) is need to the excavate this pit?

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