# Examples for 8th grade - page 71

- Cablecar

Funicular on Petrin (Prague) was 408 meters long and overcomes the difference 106 meters in altitude. Calculate the angle of climb. - Three friends

Three friends divided the profit 104,650 CZK, so that for every 4 CZK, which got the first friend equals 5 crowns for second and for every 9 CZK, which got the second equals 16 CZK for third. Question: Who got the most and how much. - Concrete pipe

How much will cost cover a 6 m long concrete pipe with an outer radius 1.5 m and inner radius 0.8 meters if 1 m^{2}paint costs 24 €. - Store

Peter paid in store 3 euros more than half the amount that was on arrival to the store. When he leave shop he left 10 euros. How many euros he had upon arrival to the store? - Internal angles

One internal angle of the triangle JAR is 25 degrees. The difference is the size of the two other is 15°. Identify the size of these angles. - Costume

Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand De - Six years

In six years Jan will be twice as old as he was six years ago. How old is he? - Rectangle - sides 4

Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5. - Mom and daughter

Mother is 39 years old. Her daughter is 15 years. For many years will mother be four times older than the daughter? - Water channel

The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow - The factory

The factory ordered 500 hexagonal steel bars of square section with 25 mm side. How many cars with a load capacity of 3 tonnes will be needed for bars move if the steel density is 7,850 kg.m-3? - Unknown number 10

Number first increased by 30%, then by 1/5. What percentage we've increased the original number? - Sum 10

What is the probability that two dice throw twice in a row will result the sum of 10? - Three digits number 2

Find the number of all three-digit positive integers that can be put together from digits 1,2,3,4 and which are subject to the same time has the following conditions: on one positions is one of the numbers 1,3,4, on the place of hundreds 4 or 2. - Mirror

How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm and Paul is from the tower distant 20 m. - Divisibility by 12

Replace the letters A and B by digits so that the resulting number x is divisible by twelve /find all options/. x = 2A3B How many are the overall solutions? - Pet store

In a pet store, they are selling out the fish from one aquarium. Ondra wanted half of all fish, but they don't wish cut by hal fany fish he got one more than demanded. Matthew wished the remaining half of the fish, but as Andrew got half the fish more th - Steamer

At 6 hours 40 minutes steamer sailed from the port at speed 12 km/h. At exactly 10 hours started sail motorboat at speed 42 km/h. When motorboat will catch steamer? - Four sided prism

Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane. - Right triangle eq2

Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.

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