Minimum + derivation - examples

  1. Sphere in cone
    sphere-in-cone A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
  2. Sphere and cone
    cone_in_sphere Within the sphere of radius G = 26 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
  3. Statue
    michelangelo On the pedestal high 2.3 m is statue 3.3 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.5 m.
  4. Ladder
    rebrik_4 4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall?
  5. Cone
    diag22 Into rotating cone with dimensions r = 18 cm and h = 17 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.
  6. Paper box
    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?
  7. Minimum of sum
    derive_1 Find a positive number that the sum of the number and its inverted value was minimal.

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