# Examples for 9th grade - page 4

- 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? - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 38 cm and 55 cm long. - Cube diagonal

Determine length of the cube diagonal with edge 33 km. - 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. - Regular 5-gon

Calculate area of the regular pentagon with side 7 cm. - 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? - 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? - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - 7 heroes

9 heroes galloping on 9 horses behind. How many ways can sort them behind? - Rhombus ABCD

Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD. - Diagonal

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

Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material, if it weigh is 2.4 kg? - Area of RT

Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 4. - Pipes

Water pipe has a cross-section 1405 cm^{2}. An hour has passed 756 m^{3}of water. How much water flows through the pipe with cross-section 300 cm^{2}per 15 hours if water flow same speed? - Vinegar 2

How many percentage of getvinegar solution, if we mix to 2 liters of 5.9% and 2 liters of 3.5% vinegar? - Circles

The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle. - Two cars

Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet?

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