Examples for 8th grade - page 22
What is the perimerer of a right triangle with the cathetuses 20 cm and 13 cm?
The perimeter of the rectangle is 22 cm and content area 30 cm2. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
One half of rope use Mam for packaging, half of the rest got son, half of the rest he took father and two fifths of what remained, got daughter. Remained 52 cm of rope. How long was rope at the beginning?
Surfaces of cubes, one of which has an edge of 18 cm shorter than the other, differ by 7776 mm2. Determine the length of the edges of this cubes.
- Four pupils
Four pupils divided $ 1938 so that the second received 20% less than the first, the third 1/6 less than a fourth and fourth $ 132 less than the first. How much money had each of them?
Rhombus has two diagonals e=11 dm and f=17 dm. Calculate the side angle and height of the rhombus.
- Monty Hall
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. W
- Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
- Sphere - parts
Calculate the area of a spherical cap, which is part of an area with base radius ρ = 10 cm and a height v = 2.7 cm.
In 7 hours started from town Krnov truck at speed 40 km/h. Passenger car started against it in 8 hours 30 minutes from the city of Jihlava at speed 70 km/h. Distance between this two cities is 225 km. At what time and at what distance from Krnov this two.
- Train from Prague
First train from Prague started at 8:00 hour at 40 kilometers per hour. Train from Ostrava started at 9:20 at 80 km per hour. In how many hours and how far from cities with trains meet if the distance of cities is 400 km.
- Two workers
The first worker completed the task by himself in 9 hours, the second in 18 hours. After two hours of joint work left first worker to a doctor and the second finished the job himself. How many hours worked second worker himself?
There is 28 students in a class. From mathematics was'nt worse mark than 2. Average mark in mathematics was 1.4643. How many students have mark 1 and how many mark 2?
- Area codes
How many 6 digit area codes are possible if the first number can't be zero?
In a circle with radius r=11 cm is chord 4× longer than its distance from the center. What is the length of the chord?
- Rhombus base
Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u1 = 22 cm and u2 = 15 cm. Prism height is twice base edge length.
At the pharmacy are in one container 20% solution in the second 50% solution of disinfectant. They need to prepare 24 L of 36-percent solution. What amount of solution from each container is needed to mix?
9.A to attend more than 20 students but fewer than 40 students. A third of the pupils wrote a math test to mark 1, the sixth to mark 2, the ninth to mark 3. No one gets mark 4. How many students of class 9.A wrote a test to mark 5?
Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 352 dm and the other diagonal BD has length 148 dm.
- Hexagon 5
The distance of parallel sides of regular hexagonal is 81 cm. Calculate the length of the radius of the circle described to this hexagon.