Triangle + derivation - math problems
Number of problems found: 7
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. In order not to attract 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?
- 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. Find the container's radius r (and height h) so that they can hide the largest possible treasure.
4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diago
Meadow is a circle with a radius r = 19 m. How long must a rope tie a goat to the pin on the perimeter of the meadow to allow the goat to eat half of the meadow?
- 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?
See also our trigonometric triangle calculator. Triangle Problems. Derivation - math problems.