Volume + maximum - practice problems - last page
Number of problems found: 34
- Sand
The maximum weight of the car is 5000 kg. We must transfer 10 m³ of sand. How many times does a car have to go? (density of sand is 1500 kg/m3) - Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm³. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container. - Railway wagon
The railway wagon holds a 75 m³ load. The wagon can carry a maximum weight of 30 tonnes. What is the maximum density that may have material with which we could fill this whole wagon? b) what amount of peat (density 350 kg/m3) can carry 15 wagon - Paper box
The hard rectangular paper has dimensions of 60 cm and 28 cm. We cut off the corners into equal squares, and the residue was bent to form an open box. How long must beside the squares be the largest volume of the box?
- 9-year-old 4103
The package leaflet for the patient states that the medicine contains 7.5 mg of salt per ml solution (1 ml = 15 drops). Dosage of the drug for children is up to 4 years - maximum of four drops, from 4 to 10 years - 5 to 10 drops, over ten years - 11 to 20 - Measuring cork
Simon boasted that he had taken away a block of cork measuring 0.5m x 0.5m x 1.2m. Is it possible if we know that 1 m of cubic cork weighs 300 kg and children from 10 to 15 years old can carry a maximum load of 5 kg? - Lathe
Calculate the percentage of waste if the cube with 53 cm long edge is lathed to the cylinder with a maximum volume. - Milk package
Milk is sold in a box with dimensions of 9.5 cm, 16.5 cm, and 6.5 cm. Determine the maximum amount of milk that can fit into a box. Coating thickness is negligible. - Max - cone
The workshop must produce the greatest cone from the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, and 6.2 cm. a) Calculate cone volume. b) Calculate the waste.
- Pumps
Pump drawing water at velocity 3.5 liters per second from a construction trench takes 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity you would - Cone
Into rotating cone with dimensions r = 8 cm and h = 8 cm is an inscribed cylinder with maximum volume so that the cylinder axis is perpendicular to the cone's axis. Determine the dimensions of the cylinder. - Cross-sections of a cone
Cone with base radius 16 cm and height 11 cm divided by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body. - Car range
Calculate the maximum range of cars, if you can spend 10 euros, the diesel price is 1.55 Eur/l, and car consumption is 3 l/100 km. - Lathe
From the cube of edge, 37 cm was a lathed maximum cylinder. What percentage of the cube is left as waste after being lathed?
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