# Examples for 8th grade - page 102

1. Regular prism
The regular four-sided prism has a base of 25 cm2 and a surface of 210 cm2. Find its volume.
2. Inscribed
Cube is inscribed in the cube. Determine its volume if the edge of the cube is 10 cm long.
3. Tangent 3
In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.
4. Twelve
Twelve students work on a week forestry brigade. One hundred spruces will receive x CZK, one hundred pine y CZK. How many receive each one students did in one day if they planted a total of 25,000 spruces per week and 30,000 pine trees? Express by expressi
5. Klara
Klara and Jitka went on a hiking trip at 13 o'clock at speed 5km/h. At 14 o'clock, Tomas ride on the bike at an average speed of 28 km/h. How many hours and at what distance from the beginning of the road Tomáš caught the two girls?
6. Composite ratio
Jakub, Aneta, and Lenka divided 1342 USD in the ratio 5/2: 3/10: 1/4. How much did Lenka take?
7. Fractions
Three-quarters of an unknown number are 4/5. What is 5/6 of this unknown number?
8. Test points
If you earned 80% of the possible 40 points, how many points did you miss to get 100%?
9. Sixty
Sixty percent of one-fifteen of the total is equal to thirty. What are two percent of the total?
10. Container
The container-shaped box with internal dimensions of 3.9 m, 3.25 m and 2.6 m was completely filled with goods in the same cubic boxes. How long edge could this box have?
11. The farmer
The farmer had 140 sheep. For the next year, she decided to change the number of sheep in ratio 10: 7. How many sheep will he have then?
12. Profit per kilo
The trader sells apples at a profit of 20% per kilogram. Today, he decided to reduce the price of apples by 10%. How much profit does the trader have today?
13. Find the 3
Find the distance and mid-point between A(1,2) and B(5,5).
14. Electric input power
Solve problems related to electric power: a) U = 120 V, I = 0.5 A, P =? b) P = 200 W, U = 230 V, I =? c) I = 5 A, P = 2200W, U =?
15. Overtaking
On the direct road, the passenger car overtakes the slower bus by starting to overtake 20 meters from the bus and after passing it ahead of it again 20 meters away. The car overtakes at a steady speed of 72 km/h, the bus goes at a steady speed of 54 km/h..
16. Triplets
Three years ago, the triplets Pavel, Petr, and Luke and their five-year-old sister Jane had together 25 years. How old is Jane today?
17. Height as diameter of base
The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.
18. Seawater
Seawater has a density of 1025 kg/m3, ice 920 kg/m3. 8 liters of seawater froze and created a cube. Calculate the size of the cube edge.
19. 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.
20. Square
Square JKLM has sides of length 24 cm. Point S is the center of LM. Calculate the area of the quadrant JKSM in cm2.

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