Pythagorean theorem + derivation - practice problems
Number of problems found: 7
- Carpet
The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make a rectangular cut of a roll. That piece of carpet will be the longest possible and will fit into the room. How long is a piece of carpet? Note: The carpet will not be parallel w - 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. - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. To avoid attracting attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal? - 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? - 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? - Ladder
A 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
We apologize, but in this category are not a lot of examples.
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