# Examples for 9th grade - page 4

1. Cubes One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
2. Discount Ladies sweater was twice discounted. First by 11%, then by 11% of the new price. Its final price was 100 €. Determine the original price of sweater.
3. Transforming cuboid Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
4. Cone A2V Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
5. Rhombus Calculate the perimeter and area of ​​a rhombus whose diagonals are 38 cm and 55 cm long.
6. Short cut Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 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?
7. Gimli Glider Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long it takes to plane from engine failure to hit the ground. Ca
8. River From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
9. 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 cm2. What scale is the city plan?
10. Cube diagonal Determine the length of the cube diagonal with edge 75 mm.
11. Regular 5-gon Calculate area of the regular pentagon with side 7 cm.
12. Logs Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
13. Sphere The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
14. Right triangle Alef The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
15. Rectangle In rectangle with sides, 6 and 3 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?
16. No. of divisors How many different divisors have number ??
17. Proof PT Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
18. 7 heroes 9 heroes galloping on 9 horses behind. How many ways can sort them behind?
19. Vinegar 2 How many percentage of getvinegar solution, if we mix to 3.5 liters of 5.8% and 5 liters of 7.6% vinegar?
20. Rhombus ABCD Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.

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