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?

Correct answer:

A =  293.9388 °

Step-by-step explanation:

s=1  V=13 π r2 h  h=s2r2 V=13 π r2 s2r2 V=13 π r2 1r2  V=0 V=dVdr=πr(23 r2)3 1r2 r>0;r1  23 r2=0 r=2/30.8165  o1=2π r=2 3.1416 0.81655.1302 o2=2π s=2 3.1416 16.2832  A=360 o1o2=360 5.13026.2832=120 6=293.9388=2935620"



We will be pleased if You send us any improvements to this math problem. Thank you!






avatar




Tips to related online calculators
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
Tip: Our volume units converter will help you with the conversion of volume units.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions:

  • Cone A2V
    popcorn The surface of the cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  • Circular sector
    vysek_circle I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
  • Cut and cone
    kuzel Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
  • Circle section
    circle_segment Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector and
  • Circle sector
    vysec Circular sector with a central angle 160° has area 452 cm2. Calculate its radius r.
  • Circular segment
    odsek Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ)
  • Sphere and cone
    cone_in_sphere 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?
  • Martians
    sphere_in_cone.png 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?
  • Circular pool
    arc_open The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?
  • Cone side
    kuzel3 Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
  • Sector
    vysec The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.
  • The central
    sector The central angle of a sector is 30° and the radius is 15 m. Determine its perimeter.
  • Axial section
    cone2 The axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
  • Volume of the cone
    kuzel2 Calculate the volume of the cone if the content of its base is 78.5 cm2 and the content of the shell is 219.8 cm2.
  • Right circular cone
    cut-cone The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
  • Hexagon rotation
    hexagnos A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
  • Circle arc
    pizza Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of the central angle.