# Examples for 9th grade - page 4

- Logs

Trunk diameter is 79 cm. Is it possible to inscribe a square prism with side 75 cm? - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 15 cm and 27 cm long. - Sphere

Surface of the sphere is 2260 cm^{2,}weight is 52.2 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 10 and 9 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| = 42 cm, |BD| = 96 cm. Calculate the perimeter of the rhombus ABCD. - Diagonal

Calculate the length of the diagonal of the rectangle ABCD with sides a = 6 cm, b = 7 cm. - Area of RT

Calculate the area of a right triangle which hypotenuse has length 20 and one hypotenuse segment has lenght 15. - Two cars

Two cars started against each other at the same time to journey long 225 km. First car went 35 km/h and second 48 km/h. What distance will be between this cars 20 minutes before meet? - Circles

The areas of the two circles are in the ratio 1:15. The larger circle has diameter 25. Calculate the radius of the smaller circle. - 7 heroes

5 heroes galloping on 5 horses behind. How many ways can sort them behind? - 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 4.8 kg? - Pipes

Water pipe has a cross-section 1420 cm^{2.}An hour has passed 831 m^{3}of water. How much water flows through the pipe with cross-section 300 cm^{2}per 8 hours if water flow same speed? - Widescreen monitor

Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 37 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha - Forces

In point X acts three orthogonal forces: F_{1}= 13 N, F_{2}= 8 N and F_{3}= 15 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Tanks

Fire tank has cuboid shape with a rectangular floor measuring 11 m × 14.3 m. Water depth is 1.3 m. Water was pumped from the tank into barrels with a capacity of 3.9 hl. How many barrels were used, if the water level in the tank fallen 3 cm? Wri - Vinegar 2

How many percentage of getvinegar solution, if we mix to 14.5 liters of 7.8% and 2.5 liters of 5.8% vinegar? - Cylinders

Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much? - Circle arc

Circle segment has a circumference of 13.26 mm and 252.03 mm^{2}area. Calculate the radius of the circle and size of central angle.

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