# Examples for 8th grade - page 97

1. 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.
2. Find the
Find the volume of a quadrangle prism high 2dm whose base is a square with a side 15cm.
3. Interior designer
To make draperies an interior designer needs 11 1/4 yards of material for the den and 8 1/2 yards for the living room. If material comes only in 20 yard bolts, how much will be left over after completing both sets of draperies?
4. Together
Grandfather, father, and son are carpenters. They decided to make a wardrobe. Father produces it for 12 hours, his son for 15 hours, and grandfather for 10 hours. How long will they make it together?
5. In and out
The empty tank is filled in 12 minutes and empty in 16 minutes. How long does it take to fill if we forgot to close the drain? If the tank has 1000 l.
6. 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. They
7. The ball
The ball was discounted by 10 percent and then again by 30 percent. How many percent of the original price is now?
8. Sick
Six seamstresses should make 60 shirts in five business days. After three days two seamstresses were sick. How many days have the remaining seamstresses to finish contract?
9. 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?
10. Two friends
Peter can do all his work himself in 6 hours. Martin can do the same work himself in 8 hours. Peter worked first and then replaced by Martin. Whole work was done in 6.5 hours. Calculate how long Peter worked before replaced by Martin.
11. Equilateral triangle
Calculate the area of an equilateral triangle with circumference 72cm.
12. Gasoline tank 2
A gasoline tank is 1/6 full. When 25 liters of gasoline were added, it became 3/4 full. How many liters more is needed to fill it? Show your solution.
13. Sand path
How many m3 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?
14. Three machines
The power of the three machines is 2: 3: 5. Two most powerful machines produce 400 parts per hour. How many components make all three machines in 3 hours?
15. A clock
A clock was set right at 6:00 AM. If it gains 3 1/2 minutes per hour, what time will it show at 6:00 PM on the same day? Show your solution
16. Bamboo
Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken?
17. Vehicle tank
A vehicle tank was 3/5 full of petrol. When 21 liters of fuel was added it was 5/6 full. How many liters of petrol can the tank hold?
18. 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 cm2. What dimensions can this large rectangle have? Write all options. Explain your calcu
19. Finding the base
Find unknown base of percent: 12.5 percent of what = 16 ?
20. Supermarket 2
A supermarket had a buko pie sale. In the morning 2/3 of the pies were sold and in the afternoon 1/6 of the pies were sold. If 150 pies were left, how many pies had been sold? Show your solution.

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