# The most difficult examples - page 5

- Church tower

Archdeacon church in Usti nad Labem has diverted tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Result write in degree's minutes. - Land - isosceles trapezoid

Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m. - Tree shadow 3

What is the diameter of a tree around which is 3m 9dm 7cm long rope wrapped? How big is its cross-sectional area? - 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. - Paper collecting

At the paper collecting contest gathered Franta 2/9 ton, Karel 1/4 ton and Patrick 19/36 tons of paper. Who have gathered the most and the least (x, y - write down the weights in tonnes). - Diagonals of diamond

Find the area and circumference of the diamond ABCD with 15m and 11m diagonals. - Cone and the ratio

Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface. - Pyramid

Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC. - Prism

Find the volume and surface area of prism with base of an equilateral triangle with side 7 dm long and the body height of 1.5 m. - The cellar

Mr Novák has a cellar and a cellar window in the chalet has 0.6 meter square window. The window wishes to place an X-shaped grid in a square. He uses iron welded bars. Calculate the lengths of individual bars and what the total length of the bars he has t - Prism

Base of perpendicular triangular prism is a right triangle with cathetuses 4.5 cm and 6 cm. What is the surface of the prism, if its volume of 54 cubic centimeters. - 30-gon

At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area. - Gasoline canisters

35 liters of gasoline is to be divided into 4 canisters so that in the third canister will have 5 liters less than in the first canister, the fourth canister 10 liters more than the third canister and the second canister half of that in the first canist - Unknown number

I think number. If subtract from the twelfth square the ninth square I get a number 27 times greater than the intended number. What is this unknown number? - Two triangles SSA

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles. A = 59°, a = 13, b = 14 - The tram

The tram is moving with acceleration a = 0.3m/s2. How long it will pass the first meter of track? How long does it take 10 meters. What is its speed at the end of the 10 meters track? - Sebastian

From Kovalov Sebastian walks at 6 km / h started at 8:00 in the direction of Kuty. From Kuty, the godfather is driving at 50 km/h and started at 8:30. The distance is 24 km. When and where grandfather will take Sebastian to the car. - Pentagon

Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm. - Hexagon area

The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area. - Trapezium internal angles

A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D.

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