# Grade - examples - page 76

1. Total displacement
Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back.
2. Gravel - cone
Mound of gravel has shape of regular circular cone with a height 3.3 meter and a base circumference of 18.85 meters. How many cubic meters of gravel are in the pile? Calculate the weight of gravel if its density is p = 640 kg / cubic m.
3. Deposit 3
After a year had Martin on bank account € 2028. What was the interest rate when the initial deposit was € 1879?
4. Clocks
How long track travel the second hand in 46 hours, the end of which is 4 cm long.
5. Two pumps
The first pump fills the tank in 24 hours second pump in another 40 hours. For how long will take fill the tank if operate both pumps at the same time?
6. Tractors
6 tractors started plowing the field that them together take 12 days. Agronomist hesitates to A) after 2 days to withdraw 2 tractors, or B) after 3 days to withdraw 3 tractors. Help him which of these two cases will be plowing done sooner.
7. Triangle SSA
Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
8. Bakery
How heavy must prepare bread at a bakery if lose during baking 16% of water and after baking must have 2 kg? (Calculate to the nearest gram)
9. Olympics
In how many ways can be placed 6 athletes on the podium at the Olympics? Depend on the color of the metal.
10. Circular flowerbed
Circular flowerbed with diameter 8 m we split by concentric circle to circle and annulus with the same area. Determine the radius of the circle.
11. Buing
Brother got to buy 240 CZK and could buy for 1/8 what he wanted. Could he pay the rest of the purchase for 200 CZK?
12. Apples
A 2 kg of apples cost a certain sum of money. This sum is equal to the amount of kilograms for which we pay 72 CZK. How much is 1 kg of apples?
13. Hexagonal pyramid
Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
14. Triangle ABC
In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
15. Bottle
Bottle with wine costs 58 USD. Wine is 27 USD more expensive than the empty bottle. How much is the bottle itself?
16. Dig water well
Mr. Zeman digging a well. Its diameter is 120 cm, and plans to 3.5 meters deep. How long (at least) must be a ladder, after which Mr. Zeman would have eventually come out?