Volume + minimum - practice problems
Number of problems found: 20
- Tent - spherical cap
I have a tent in the shape of a spherical cap. Assume we want the volume to be 4 cubic meters, to sleep two or three people. Assume that the material making up the dome of the ten is twice as expensive per square as the material touching the ground. What - Container 81972
There are 45 liters of water in a 50-liter container. How many liters of water will it contain if we add another 10 liters of water to it? - The pilot
The pilot is on a mission with 160 liters of fuel. The distance between the main base and the operation area is 2 hours. The distance between the main base and backup base is 1 hour. Assume: - Aircraft fuel consumption is 10 lt/h. - Minimum fuel after lan - Joanne 2
Joanne bought five fish. For fish to have enough space, they must have at least 30 liters of water. You know that the length is 5 dm and the width is 3 dm. Calculate the minimum height of the aquarium.
- Processing 65514
The Nováková family took a loan (loan) of 120,000 euros from the bank. What was the amount of the fee for processing, setting up, and providing the loan if, according to the bank's fee schedule, it is 0.80% of the loan volume, but at least 250 euros and a - The volleyball ball
The volleyball ball can have a circumference of at least 650 max 750 mm after inflation. What air volume can this ball hold if its circumference is the average of the minimum and maximum inflation of the ball? - Largest possible cone
It is necessary to make the largest possible cone from an iron rod in the shape of a prism with dimensions of 5.6 cm, 4.8 cm, and 7.2 cm. a) Calculate its volume. b) Calculate the waste. - Iglu - cone tent
The cone-shaped tent is 3 m high, and the diameter of its base is 3.2 m. a) The tent is made of two layers of material. How many m² of fabric is needed for production (including flooring) if 20% needs to be added to the minimum amount due to cutting waste - The wooden
The wooden block measures 12 cm, 24 cm, and 30 cm. Peter wants to cut it into several identical cubes. At least how many cubes can he get?
- Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Block-shaped 7976
A block-shaped pool with a volume of 200m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Diameter 7648
The mug has the shape of a cylinder with a height of 60.7 mm. There is two dl of water in it. If we dip a ball with a diameter of 40 cm into the water, the water will not overflow. What is the minimum diameter of the cup? - Minimum surface
Find the length, breadth, and height of the cuboid-shaped box with a minimum surface area, into which 50 cuboid-shaped blocks, each with length, breadth, and height equal to 4 cm, 3 cm, and 2 cm, respectively, can be packed. - Cylindrical 6636
A cylindrical container with a bottom diameter of 30 cm and a height of 20 cm is filled with water. We want to pour the water into another cylindrical container with a bottom diameter of 15 cm. What minimum height must the second container have for the wa
- 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. - 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? - Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - 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. - Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone?
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