# Examples for 8th grade - page 18

- Mystery of stereometrie

Two regular tetrahedrons have surfaces 48 cm^{2}and 108 cm^{2.}In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - Cyclist

A cyclist is moving at 26 km/h and follow pedestrian who is walking at speed 7 km/h. Walker has an advantage 13 km. How long take cyclist to catch up with him? - Elevation

What must be the elevation of an observer in order that he may be able to see an object on the earth 814 km away? Assume the earth to be a smooth sphere with radius 6378.1 km. - AVG of INT

What is the average of the integers from 7 throuht 15 inclusive? - Slope of the pool

Calculate slope (rise:run) of the bottom of swimming pool long 40 m. Water depth at beginning of pool is 1.15 m (for children) and depth at end is 1.92 m (for swimmers). Slope express as percentage and as angle in degrees. - Glass mosaic

How many dm^{2}glass is nessesary to produc 50 slides of a regular 6-gon, whose side has length 7 cm? Assume that cutting glass waste is 14%. - Hiker

Hiker went half of trip the first day, the third of trip the second day and remaines 13 km. How long trip he planned? - Discounts on rail (ZSSK)

The railway company ZSSK offers a discount of 40% (JUNIOR RAILPLUS EURO - Square grid

Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm^{2}and circumference 12 cm and that their sides is in square grid. - Fertilizer

Mr. Gherkin use for fertilization 9% solution of fertilizer. 7 liters of it still left. How much water must be added to the solution to make only 5% solution? - Map

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

Pit has shape of a truncated pyramid with rectangular bases and is 2.8 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.3 l of green colour. How many liters of paint is needed when w - Water tank

Water tank shape cuboid has a width of 3.3 m and length twice larger. How high will reach water if water flow into 15 liters of water per second during 23 minutes? - Root

Use law of square roots roots: ? - Intersections

How many intersections have circles with radius 12 dm and 17 dm, if the distance of their centers is 20 dm. - Lock

Combination lock will open when the right choice of 5 numbers (from 1 to 12 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately? - Event probability

The probability of event G in 9 independent experiments is 0.48. What is the probability that the event G occurs in one experiment (probability is same)? - Plan of the village

Plan of the municipality in 1:1000 scale has plotted garden with dimensions 25 mm and 28 mm. Determine the area of gardens in ares in reality. - Dices

We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2? - Shots

2000 lead shots with diameter 2 mm is decanted into a ball. What is it diameter?

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