Examples for 9th grade - page 30
- Rotating cone II
Calculate area of surface of rotating cone with base radius r=7 cm and height h=17 cm.
- Geometric mean
Calculate the geometric mean of numbers a=23.4 and b=16.8. Determine the mean by construction where a and b are the length of the lines.
- Hollow sphere
Calculate the weight of a hollow brass sphere (density 8.5 g/cm3), if the outer diameter is 10 cm and wall thickness is 3 mm.
Peter and Stano lawn grass for 3 hours 12 minutes. How long would it take to Peter if Stano lawn grass himself for 384 minutes.
- Four swords
Obelix has three helmets, four swords and five shields. How many swords must make at the blacksmith forge Metallurgix to be able to walk another 90 days in unique armor?
- Football season
Dalibor and Adam together scored 97 goals in the season. Adam scored 9 goals more than Dalibor. How many goals scored each?
We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How much of this two types of candy is necessary to prepare this mixture?
- AP 6
Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
- Triangular prism
Base of perpendicular triangular prism is a right triangle with leg length 5 cm. Content area of the largest side wall of its surface is 130 cm² and the height of the body is 10 cm. Calculate its volume.
- AP - simple
Determine the first nine elements of sequence if a10 = -1 and d = 4
Welder do the job for six hours, the second one for 8 hours. How long do the job third welder if all together can do job in 2 hours?
- Tetrahedral prism
The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge, if you know that the prism volume is 2187 cm3.
- Cube and water
How many liters of water can fit into a cube with an edge length of 0.11 m?
Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ?
- Pages of book
Lenka calculated that if every day to read 16 pages of the book, read a book a day earlier than had read only 14 pages a day. How many pages has this book?
- Tetrahedral prism
Calculate surface and volume tetrahedral prism, which has a rhomboid-shaped base, and its dimensions are: a = 12 cm, b = 7 cm, ha = 6 cm and prism height h = 10 cm.
- Cars motion
From point A car start at the speed of 90 km/h. Against it departs from the point B at the same time another car at 60 km/h. For how long and where they met if the distance between A and B is 180 km?
- Supplementary angles
One of the supplementary angles are three times larger than the other. What size is larger of supplementary angles?
- Little hand
What angle shifted little hand on the clock after one hour and 38 minutes?
The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?