# Examples for 8th grade

- Filament of bulb

The filament of bulb has a 1 ohm resistivity and is connected to a voltage 220 V. How much electric charge will pass through the fiber when the electric current passes for 10 seconds? - Pendulum

Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm. - Volume and body diagonal

Calculate how much the volume and body diagonal of the cuboid decrease if we reduce each of its three edges a, b, c by 18%? - Garden fence

The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced? - Two unknown numbers

One number is 2 less than a second number. Twice the second number is 14 less than 5 times the first. Find the two numbers. - Endless lego set

The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. The - Highway tunnel

The highway tunnel was built from two ends in the north-south direction. The average daily performance of the "northern party" rasters was higher than the average daily power of the "southern party" of the rasters. After 55 business days, both parties met - The pole

The telegraph pole is supported by a 4 m bullet at 3/4 of its height, the end of which is at a distance 2.5 m from the pole post. Calculate the height of the telegraph pole. - Two workers

Two workers should fulfill certain task together for 5 days. If the first worker increased their performance twice and second twice fell, it took them just four days. For how many days would handle the entire task first worker himself? - Seamstress

The seamstress cut the fabric into 3 parts. The first part was the eighth fabric, the second part was three-fifths of the fabric and the third part had a length of 66 cm. Calculate the original length of the fabric. - T-shirts and hat

5 t-shirts and a hat cost £62.00 2 t-shirts and a hat cost £29.00 How much does a t-shirt cost ? How much does a hat cost ? - Unknown number

If I reduced the sum of the numbers 70 and the unknown number three times, I would get 100. what is the unknown number? - Train delay

The train should be in the station for 10 minutes. It still has 32 km left. What is the expected delay if the train travels in 2 minutes 3 km except for the last section where it is 2 km in 5 minutes. - Conical area

A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation. - Fence and scale

The garden with 80 m of fencing is draw on plan as a square with a side length of 4 cm. At what scale is this plan made? - Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =? - Substitution

solve equations by substitution: x+y= 11 y=5x-25 - Unknown numbers

The sum of two consecutive natural numbers and their triple is 92. Find these numbers. - Tangent

What distance is the tangent t of the circle (S, 4 cm) and the chord of this circle, which is 6 cm long and parallel to the tangent t? - Simple equations

Solve system of equations: 5x+3y=5 5x+7y=25

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