# Examples for 8th grade - page 4

- Cuboid

The cuboid has a surface area 7086 cm^{2,}the length of its edges are in the ratio 4:2:1. Calculate the volume of the cuboid. - Pool

The swimming pool is 10 m wide and 22 m long and 191 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge. - Bus vs. train

Bus started from point A 10 minutes before the train started from the same place. The bus went an average speed of 49 km/h, train 77 km/h. To point B train and bus arrived simultaneously. Calculate time of train journey, if train and bus travelled the. - Triangle SAS

Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=21 and height v=7? - Is right?

Is triangle with sides 51, 56 and 77 right triangle? - Square

Points A[-9,6] and B[-5,-3] are adjacent vertices of the square ABCD. Calculate area of the square ABCD. - Movement

From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 24 km/h, the second at average speed 26 km/h. Determine the distance between them after 35 minutes cycling. - Gimli Glider

Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1870 feet and maintain constant speed 212 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate - Short cut

Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field? - Scale

Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm^{2.}What scale is the city plan? - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm^{2.}Calculate the volume of a cone. - River

From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river. - Cube diagonal

Determine length of the cube diagonal with edge 33 km. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm^{2.} - Discount

Ladies sweater was twice discounted. First by 17%, then by 17% of the new price. Its final price was 70 USD. Determine the original price of sweater. - Regular 5-gon

Calculate area of the regular pentagon with side 7 cm. - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 2 cm and 6 cm long. - Logs

Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm? - Right triangle Alef

The area of a right triangle is 294 cm^{2,}the hypotenuse is 35 cm long. Determine the lengths of the legs.

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