# Examples for 8th grade

- The big clock

The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00? b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00 - Two rectangles

I cut out two rectangles with 54 cm², 90 cm². Their sides are expressed in whole centimeters. If I put these rectangles together I get a rectangle with an area of 144 cm^{2}. What dimensions can this large rectangle have? Write all options. Explain your calc - Two heights and a side

Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm and height to side b: vb = 4 cm. - Glass with icecream

We have 6 kinds of ice cream and 5 kinds of fruit. We put 3 cups of ice cream and 2 fruits into each glass. How many can unique decorated glasses be? - 40% volume

40% volume with 104 uph (units per labor hour) 8 people working. What is the volume? - Regular prism

The regular four-sided prism has a base of 25 cm^{2}and a surface of 210 cm^{2}. Find its volume. - Performance

Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together? - Bulbs and electricity

In the sports hall, 875 identical light bulbs light for 2 hours. How long does it take for 100 such light bulbs to consume the same amount of electricity? - Angle of diagonal

Angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10cm. Calculate the body volume. - Sand path

How many m^{3}of sand is needed to fill the 1.5m wide path around a rectangular flowerbed of 8m and 14m if the sand layer is 6cm high? - An oil

An oil drum is cut in half. One half is used as a water trough. Use the dimensions; length 82cm, width 56cm to estimate the capacity of the water trough in liters. - Equilateral cylinder

A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere. - Scientific notation

Approximately 7.5x10^{5}gallons of water flow over a waterfall each second. There are 8.6x10^{4}seconds in 1 day. Select the approximate number of gallons of water that flow over the waterfall in 1 day. - Resistance

A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor. - Lampshade

The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm^{2}of material will we need when we 10% is waste? - Triangles

Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle? - Simplify 2

Simplify expression: 5ab-7+3ba-9 - Ditch

Ditch profile is an isosceles trapezoid with bases of length 80m and 60m. The slope of the side wall of the ditch is 80°. Calculate the ditch depth. - 15 teachers

15 teachers teach for a combined amount of 128 days over a period of 64 days. What is this expressed as a percentage? - Area of iso-trap

Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other.

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