# Examples for 8th grade - page 60

- Similarity

ABC is a triangle wherein a = 4 cm, b = 6 cm, c = 8 cm. Is it similar to the triangle DEF: d = 3 cm, e = 4.5 cm, f = 6 cm? If so, determine the ratio of similarity. - Cube containers

Two containers shaped of cube with edges of 0.7 m and 0.9 m replace a single cube so that it has the same volume as the original two together. What is the length of the edges of the new cube? - Salt

1 t of sea water contains 25 kg of salt. How many tons of seawater must be evaporated to obtain 2 q of salt? - Painters

15 painters painted fence for 280 minutes. For how many minutes paint half of this fence 12 painters? - Cuboid - volume, diagonals

The length of the one base edge of cuboid a is 3 cm. Body diagonal is ut=13 cm and diagonal of cuboid's baseis u1=5 cm. What is the volume of the cuboid? - Well

Rope with a bucket is fixed on the shaft with the wheel. The shaft has a diameter 50 cm. How many meters will drop bucket when the wheels turn 15 times? - Earth's surface

The greater part of the earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land? - Rhombus and diagonals

The a rhombus area is 150 cm^{2}and the ratio of the diagonals is 3:4. Calculate the length of its height. - Resort

In a completely crowded resort was 30% from the Czech Republic quarter visitors were from Slovakia and the rest 135 came from Germany. What capacity have resort? - Work at plant

Handyman has vowed to do repair work at the plant for 25 days. However, work had to be shortened and therefore gained helper. Together they made all the corrections for 13 1/3 days. How long the work would take helper himself? - Trapezoid

How long are the trapezoid bases with area 24 cm^{2}and height 3 cm. One base is 3 times longer than the shorter. - Four classses

Students of all 7, 8 and 9 classes in one school may take up 4,5,6 and 7 abreast and nobody will left. How many is the average count of pupils in one class if there are always four classes each grade? - Body diagonal

Cuboid with base 7cm x 3,9cm and body diagonal 9cm long. Find the height of the cuboid and the length of the diagonal of the base, - Three co-owners

The three co-owners of building company have earnings from a contract portioned in the ratio of 3:6:7. Each of them received the amount in whole USD. One of them on contract earned 86450 USD. What was the total earnings this order? - Brigade

On a weekly forest brigade operates 12 students. After plant one hundred spruces get x CZK, anfter one hundred pines y CZK. How many CZK got one student for one day if planted spruces 25000 and 30000 pines week? - Triangular prism

Calculate the volume and surface area of a triangular prism if it is given: a = 6.8 dm. ..Va = 4 dm. (base edge length and base triangle height length) ... ... .v = 23 dm (body height) - Cube wall

The perimeter of one cube wall is 120 meters. Calculate the surface area and the body diagonal of this cube. - The deposit

Deposit has been placed for one year at an annual rate of 4.5%. After the added interst amount rose to € 2,612.5. Determine initial deposit. - Ski class

Class attend 30 boys and some number of girls. Ski training was attended by 28 boys and all the girls, which was 95% of all students. How many girls attend this class? How many percent is that? - Surface area of cylinder

Determine the lateral surface of the rotary cylinder which is circumscribed cube with edge length 5 cm.

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