Examples for 8th grade - page 43
- Inscribed triangle
To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
- Garden pool
Mr. Novak fill garden pool (cylinder; diameter of 200 cm) with 31.4 hl of water. What is the depth of the pool when the water level is 10 cm below the upper edge of the pool?
Wheel in traction tower has a diameter 2 m. How many meters will perform an elevator cabin if wheel rotates in the same direction 66 times?
- Lamp cone
Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm.
- Concentric circles
In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.
For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle?
- Water pool
Pool with volume 990hl completely filled, if water flows by one tap 8 hours and by second tap 6 hours. First tap give 10hl more than second per hour. How many hl flows in each of them in an hour?
- Slovak broad track
Once upon a time, we learned in school that the Russians have "wider" tracks than our, because they have less tolerable ground. In truth, decide olny area of sleepers, no track gauge. Calculate how many millimeters, our track 1435 mm different from the R
The volume of tetrahedral prism is 2.43 m3. Base of prism is a parallelogram in which a side 2,5dm and height ha = 18cm. Calculate the height of the prism.
- 6 regular polygon
It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm2 (square centimeters) has a circle in which is inscribed the 6-gon.
- Lie/do not lie
The function is given by the rule f(x) = 8x+16. Determine whether point D[-1; 8] lies on this function. Solve graphically or numerically and give reasons for the your answer.
- Two trains
Two trains go at each other. First at speed 40 km/h and the second at speed 60 km/h. At what distance will be 30 minutes before they will meet?
- Right triangle
Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.
How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
- Two wine
In 2:1 mix wine solution cost 4.1 USD. In 1:2 mix wine solution cost 4.5 USD. How much cost liter of each wine?
- Water reservoir
The water reservoir is filled with one pump for 4 days by the second one for 9 days. Outlet can drain tank in 12 days. How long take fill the reservoir if both pumps are running and not closed outlet channel.
There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the garag
- Map scale
Garden has on plan on a scale of 1: 150 width 22 cm and length 35 cm. What is the real area of the garden?
If we mix 5 kg of goods of one kind and 3 kg second one, resulting mixture cost 16.50 EUR/kg. If these quantities are mixed in reverse - first three kilograms and 5 kilograms second cost of mixture is 18.50 EUR/kg. What is the price of one kg of goods of.