# Examples for 9th grade - page 30

1. RT and ratio A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?
2. Four-digit number Find also a four-digit number, which quadrupled written backwards is the same number.
3. Cube 6 Volume of the cube is 216 cm3, calculate its surface area.
4. Workman - shift The worker produces 300 components per shift. How many components would be produced in 18 shift, if his performance gradually increased every shift by 3 components?
5. Field with vegetables Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated?
6. Swing A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance?
7. Trapezoid ABCD Calculate the perimeter of trapezoid ABCD if we know the side c=15, b=19 which is also a height and side d=20.
8. Cone and cube About what percentage hase cone with base radius r larger volume than same high cube with square base with edge length r?
9. The body The body on the figure consists of cubes with an edge length 10 cm. What surface has this body?
10. Water On the lawn which has area 914 m2 rained 3 mm of water. How many liters of water rained?
11. Tickets Tickets to the zoo cost \$4 for children, \$5 for teenagers and \$6 for adults. In the high season, 1200 people come to the zoo every day. On a certain day, the total revenue at the zoo was \$5300. For every 3 teenagers, 8 children went to the zoo. How many te
12. Spirit From 55% and 80% spirit we would like to produce 0.2 kg of 60% spirit. How many of them we must use in a solution?
13. Tunnels Mice had built an underground house consisting of chambers and tunnels: • each tunnel leading from the chamber to the chamber (none is blind) • from each chamber lead just three tunnels into three distinct chambers, • from each chamber mice can get to any
14. Katy MO Kate draw triangle ABC. Middle of AB have mark as X and the center of the side AC as Y. On the side BC wants to find the point Z such that the content area of a 4gon AXZY was greatest. What part of the triangle ABC can maximally occupy 4-gon AXZY?
15. SAS triangle The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
16. Exam average Average of marks that have on the certificates students of 8.A class in mathematics is exactly 2.45. If we did not add 1 and 3 of sutdents Michael and Alena, who arrived a month ago, it would average exactly 2.5. Determine how many students have class 8.
17. Mother and daughter Three years ago mother was three times older than daughter. After nine years she will be only twice old. How old is mother (and daughter)?
18. Warehouse cars From the warehouse started truck at speed 40km/h. After 1hour 30mins started from the same place same direction a car at speed 70 km/h. For how long and at what distance from the warehouse overtake a truck?
19. Chess How many ways can select 4 fields on classic chess board with 64 fields, so that fields don't has the same color?
20. Cone container Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.

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