Volume + maximum - math problems
Number of problems found: 15
- Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
Into rotating cone with dimensions r = 8 cm and h = 8 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder.
- 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.
Calculate the percentage of waste if the cube with 53 cm long edge is lathed to cylinder with a maximum volume.
- Railway wagon
The railway wagon holds 75 m3 load. 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 wagons?
- Max - cone
From the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, 6.2 cm must be produced the greatest cone. a) Calculate cone volume. b) Calculate the waste.
- Paper box
Hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares and the residue was bent to form an open box. How long must be side of the squares to be the largest volume of the box?
- Cross-sections of a cone
Cone with base radius 16 cm and height 11 cm divide 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.
From the cube of edge, 37 cm was a lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
- Car range
Calculate the maximum range of car, if you can spend 10 euros, price of diesel is 1.55 Eur/l and car consumption is 3 l/100 km.
The maximum weight of the car is 5000 kg. 10 m3 of sand must be transferred. How many times does a car have to go? (density of sand is 1500 kg/m3)
- Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
- 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.
Allan keeps tropical fish. His aquarium is 4 feet long, 1 foot wide, and 2 feet tall. Each fish needs at least 0.5ft³ of water. What is the maximum number of fish that he can keep in the aquarium? Please show your solution. Please
Pump that draws water at velocity 3.5 liters per second water from a construction trench take 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 wo
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