Examples for 8th grade - page 71
- Tin with oil
Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
- Juice box 2
Box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm and 32 cm. If the box stay at the smallest base juice level reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below the top of the
On double-track express met with a freight train. Express travel at speed 72 km/h, a freight train at speed 36 km/h. After what time period will be from 9 km apart?
- Angles of the triangle
ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
- Concentric circles
In the circle with diameter 17 cm is constructed chord 12 cm long. Calculate the radius of a concentric circle that touches this chord.
- Three men
Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old?
- RT and ratio
Right triangle whose cathetus are in a ratio 6:17 has hypotenuse 47 m long. How long are cathetus?
- Football season
Throughout the football season gave Adam the 23 goals more than Brano and 16 goals less than Karol. Edo gave the 6 goals more Dušan. Karol gave 5 more than Edo. Brano and Edo gave together 17 goals. How many goals gave each boy and how many goals gave the.
Workers digging a jump pit in the school yard. Pit has a cuboid shape with a length 20 m, a width 20 dm and depth 36 cm. They excavate 0.4 cubic meters of soil an hour. How much time (hours and minutes) is need to the excavate this pit?
Diameter of motocycle wheel is 63 cm. How many times rotates wheel on roand long 1 km?
- Sphere - parts
Calculate the area of a spherical cap, which is part of an area with base radius ρ = 15 cm and a height v = 2.5 cm.
Dealer sell digital camera for € 384. Thirty percent of the price was his profit. After some time, decreased interest in selling the camera and therefore reduce its sales price by 15 %. How many percent of the new price now is dealer's profit? Round the
Blade circular saw with a diameter 42 cm turns 825 times per minute. Expresses his cutting speed in meters per minute.
From Znojmo to Brno started truck with a trailer at an average speed 55 km per hour. Against him 18 minutes later from Brno started car with an average speed of 1.2-times greater than the truck. How long and how far from Znojmo, they meet if the distanc
In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
We have three cups. In the cups we had fluid and boredom we started to shed. 1 We shed one-third of the fluid from the second glass into the first and third. 2 Then we shed one quarter cup of liquid from the first to the second and to the third. 3 Then
Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 39 cm and the edge of the base is 24 cm. The edge length of the base of the prism and height is 3:2.
How many liters of water per second can go via trough, which has a cross section of semicircle with radius 2.5 m and speed of water is 74 cm per second?
Calculate the area of what may vary rectangular, if it focused by surveyor and found the dimensions 14 x 12 m while in each of the four joint points can be position deviation 8 cm?
Calculate area of the parallelogram ABCD as shown if |AB| = 45 cm, |BC| = 23 cm and angle BAD = 30°