# Examples for 8th grade - page 28

- Gauss

Help little C.F. Gauss sum all the integers from 1 to 420. - Diamond ABCD

In the diamond ABCD is the diagonal e = 24 cm and size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond. - Cone in cube

The cube is inscribed cone. Determine the ratio of the volume of cone and cube. The ratio express as a decimal number and as percentage. - Height 2

Calculate the height of the equilateral triangle with side 38. - Complete construction

Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs. - Volume and surface

Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm^{2.} - Racing track

On the racing track circling three cars. The first passes one circuit for 8 seconds, the second for 20 seconds and a third for 8 seconds. a) Calculate number of seconds since the start to catch all three cars together for the first time again across the s - Ice cream in cone

In the ice cream cone with a diameter of 5.2 cm is 1.3 dl of ice cream. Calculate the depth of the cone. - Bomber

Bomber flies 10 km at 600 km/h. At what horizontal distance from the target, must pilot drop the bomb to hit the target? Don't care about air resistance and consider the gravitational acceleration g=9.81 m/s^{2.} - Car

The driver of a car is to get to 608 km distant city. From atlas found that 162 km will have to pass through the cities at average speed 48 km/h. Remainder of the journey pass outside the cities at average speed 116 km/h. Calculate how many hours it will t - Two diggers

There are two diggers. One digger digs a pit 46 hours second gidding 2 times faster. a) how long took to dig a pit second digger b) how long took dig together - Divers

20-member group of divers carries the air for 15 hours of diving. 4 members of the expedition sick or wasn't came. How many hours is sufficient air to other divers? - Lorry

The lorry was loaded with 18 boxes of 15 kg. How many boxes with weight 18 kg can be loaded, if total load must be same? - Cuboid 5

Calculate the weight of the cuboid with dimensions of 12 cm; 0.8 dm and 100 mm made from spruce wood (ς = 550 kg/m^{3}). - Quadrangular prism

The quadrangular prism has a volume 648 cm^{3.}Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism? - Bridge

The bridge arc has a span 232 m and height 22 m. Calculate the radius of the circle arc of this bridge. - Grandson and granddad

Grandson with grandpa they counted how many years have together. Their product is 365. How many years is the sum of their years. - Iron fence

One field of iron fence consists of 20 iron rods with square cross-section of 1.5 cm side and a long 1 meter. How much weight a field if the density of iron is 7800 kg/m^{3.} - Moon

We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth. - Two cars

From the town A to town B started two cars. The first at 7:00 at average speed 60 km per hour, the second at 10:00 at average speed 100 km per hour. The first car will not stay in B, and on the way back meet the second car at half way from A to B. At what.

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