# The most difficult examples - page 5

- Triangular prism

Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 39 degrees, |AB| = 3 cm. Calculate the volume of the prism. - Diagonals of diamond

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

Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type? - Retail

At what price bought retail 1 kg goods from wholesale, if lost in the distribution is 4% of weight of the goods and retail still have a profit of 6.3%? Goods are sold at retail for 25 euro per kg. - Surface area of cylinder

Determine the lateral surface of the rotary cylinder which is circumscribed cube with edge length 5 cm. - Four friends

Four friends shared the money. Vasek got 1/4 of the total amount. Tonda received 1/3 of the rest of the money, Joe got a half from the second residue and Jirka left 80. How much money get together? - 6 regular polygon

It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm^{2}(square centimeters) has a circle in which is inscribed the 6-gon. - 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. - 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. - 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. - 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? - Land cost

The land is worth 33295 CZK. 1st owner has 5/15, 2nd owner has 4/15, 3rd owner has 1/5 4th owner has 1/5. How much CZK each of them will receive? - 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? - Scalene triangle

Solve the triangle: A = 50°, b = 13, c = 6 - 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. - 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. - Hour salary

You work for 4 hours on a Saturday and 8 hours on Sunday. You also receive a $50 bonus. You earn $164. How much did you earn per hour? - 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 - 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). - 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

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