# Examples for 9th grade - page 4

1. Server Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%.
2. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
3. Z9-I-4 Kate thought a five-digit integer. She wrote the sum of this number and its half at the first line to the workbook. On the second line wrote a total of this number and its one fifth. On the third row she wrote a sum of this number and its one nines. Fi
4. Pool The swimming pool is 10 m wide and 8 m long and 153 cm deep. How many hectoliters of water is in it, if the water is 30 cm below its upper edge?
5. 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°.
6. Movement From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
7. Square Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
8. 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.
9. 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.
10. Transforming cuboid Cuboid with dimensions 8 cm, 13 and 16 cm is converted into a cube with the same volume. What is its edge length?
11. 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?
12. Rhombus Calculate the perimeter and area of ​​rhombus whose diagonals are 38 cm and 55 cm long.
13. 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 takes to plane from engines failure to hit ground. Calculate
14. 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?
15. 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.
16. Cube diagonal Determine length of the cube diagonal with edge 75 mm.
17. Regular 5-gon Calculate area of the regular pentagon with side 7 cm.
18. Logs Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
19. Right triangle Alef The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
20. Sphere Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?

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