# Examples for 9th grade - page 4

- 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. - 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.} - 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. - Transforming cuboid

Cuboid with dimensions 10 cm, 17 and 17 cm is converted into a cube with the same volume. What is its edge length? - 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. - Sphere

Surface of the sphere is 2820 cm^{2,}weight is 71 kg. What is its density? - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - No. of divisors

How many different divisors has number ?? - Rectangle

In rectangle with sides 3 and 10 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle? - Rhombus ABCD

Rhombus ABCD, |AC| = 97 cm, |BD| = 35 cm. Calculate the perimeter of the rhombus ABCD. - 7 heroes

5 heroes galloping on 5 horses behind. How many ways can sort them behind? - Diagonal

Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.

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