# Examples for 8th grade - page 21

- Quarter circular

The wire that is hooked around the perimeter of quarter-circular arc has length 14π+56. Determine the radius of circle arc. - Gear

Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears? - Coin

How many 20-cent coins must be put in a row that next 20-cent coins after them (above) rolled on it axis? - Map

Forest has an area of 36 ha. How much area is occupied by forest on the map at scale 1:5000? - Hockey match

The hockey match ended with result 3:1. How many different storylines may have the match? - Raffle

How many raffle tickets must be purchased by Peter in raffle with issued 200 tickets if he wants to be sure win at least 3 price? In the raffle draws 30 prices. - Painters

One painter could paint a school for 7 days. The second one for 6 days. It was necessary to paint the school in two days. Next painter was invited and all worked together. How long would this painter painted the school itself? - Pumps

First pump flows 16 liters per second into the basin by the second pump 75% of the first and by third pump half more than the second. How long will take fill basin by all three pumps simultaneously volume 15 m^{3}(cubic meters)? - Tank and water

Cylindrical tank were poured with 3.5 liters of water. If tank base diameter is 3 dm, how height is water level in? - Sisters

Sisters Hanka and Vera goes mostly tograndmother by bicycle. Journey took Hanka 30 minutes and Vera 20 minutes. How long will Vera catch up with Hanka when started from home five minutes later than Hanka? - Painters

First painter painted fence himself for 12 hours, the second painter 3 hours sooner than first, and the third painters slowest up to 20 hours. How long took them paint fence if worked together? - Bottle

Bottle with wine costs 61 USD. Wine is 11 USD more expensive than the empty bottle. How much is the bottle itself? - Workers

Workers A and B will done work together for 20 days. They worked together 18 days. Then A worker became ill and worker B finish the job alone for 11 days. If every worker was working alone, how many days took whole work for worker A and B? - Pyramid roof

1/3 of area of the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered? - Maximum area of rhombus

Calculate the interior angles at which equilateral rhombus has maximum area. - Umbrella

Can umbrella 75 cm long fit into a box of fruit? The box has dimensions of 390 mm and 510 mm. - Sales off 2

Computer monitor sold for 8400 CZK in March. In April, dealer price decreased by 798 CZK. Calculate the percentage by which the price was reduced. - Plums

In the bag was to total 193 plums. Igor took 4 plums and Mary took 4/7 from the rest. How many plums remained in the bag? - Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees). - Two workers

Two workers carry will do certain work for 12 days. After 8 days of working was one removed, and then the other finished the job alone in 10 days. For how many days would do this work alone each worker?

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