# Examples for 9th grade

- Canister

Gasoline is stored in a cuboid canister having dimensions 44.5 cm, 30 cm, 16 cm. What is the total weight of a full canister when one cubic meter of gasoline weighs 710 kg and the weight of empty canister is 1.5 kg? - Tetrahedral pyramid

It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges. - Horizontal Cylindrical Segment

How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank? - Trapezium

The area of trapezium is 35 cm^{2}. Find its altitude if the bases are 6cm and 8 cm. - Euclid theorems

Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm. - Slope

Find the slope of the line: x=t and y=1+t. - Hall

Rectangular hall will have pave by square tiles with a side length 15 cm. The hall has length 18 meters and width 3 m. How many tiles need to buy if 2 percent of the amount is disrupted during the work? - Two trains

There are two trains running the same distance. 1st train will travel it in 7 hours 21minutes. 2nd the train will travel 5 hours 57minutes and 34 seconds and it is 14 km/h faster than the first train. What are speeds of trains and how long is this railwa - A mast

A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken? - Rectangular triangle PQR

In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decima - Triangular prism

The perpendicular triangular prism is a right triangle with a 5 cm leg. The content of the largest wall of the prism is 130 cm^{2}and the body height is 10 cm. Calculate the body volume. - Circle tangent

It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p. - Grandmother

Grandmother wants to give the candies to grandchildren that when she gives 5 candy everyone 3 missing and when she gives 4 candies 3 is surplus. How many grandchildren has grandmother and how many candies has? - Cone

Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long. - Working time

At 10 hours work shift, work is done in 16 days. How many days will the work be done at 8 hours shifts? - Cuboid - edges

The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid - Hexagonal prism 2

The regular hexagonal prism has a surface of 140 cm^{2}and height of 5 cm. Calculate its volume. - The factory

The factory ordered 500 hexagonal steel bars of square section with 25 mm side. How many cars with a load capacity of 3 tonnes will be needed for bars move if the steel density is 7,850 kg.m-3? - Cube walls

Find the volume and surface area of the cube if the area of one wall is 40cm2. - Quadrangular prism

The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.

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