# Examples for 9th grade - page 30

1. Divisors
Find all divisors of number 493. How many are them?
2. Interest
Calculate how much you earn for 10 years 43000 deposit if the interest rate is 1.3% and the interest period is a quarter.
3. Circle sector
Circular sector with a central angle 80 ° has area 1257 cm2. Calculate its radius r.
4. RT and ratio
A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?
5. Cars plates
How many different licence plates can country have, given that they use 3 letters followed by 3 digits?
6. Four-digit number
Find also a four-digit number, which quadrupled written backwards is the same number.
7. 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?
8. Cube 6
Volume of the cube is 216 cm3, calculate its surface area.
9. 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?
10. 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?
11. 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.
12. 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?
13. Water
On the lawn which has area 914 m2 rained 3 mm of water. How many liters of water rained?
14. The body
The body on the figure consists of cubes with an edge length 10 cm. What surface has this body?
15. 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
16. 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?
17. SAS triangle
The triangle has two sides long 7 and 19 and included angle 36°. Calculate area of this triangle.
18. 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?
19. 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.
20. 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)?

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.