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?

Correct result:

r =  31.11 cm
h =  44 cm
V =  44602.24 cm3

Solution:

G=33 cm V=13πr2h h=G+x=33+x G2=x2+r2 r2=G2x2 V=13π(G2x2)(G+x) V=13π(G3+G2xGx2x3)  V=13π(G22Gx3x2) V=0 G22Gx3x2=0 3x266x+1089=0 3x2+66x1089=0  a=3;b=66;c=1089 D=b24ac=66243(1089)=17424 D>0  x1,2=b±D2a=66±174246 x1,2=66±1326 x1,2=11±22 x1=11 x2=33   Factored form of the equation:  3(x11)(x+33)=0   h=G+x1=33+11=44 cm r=G2x12=31.11 cm 
h=33+11=44 cm
V=13πr2h=44602.24 cm3

Our quadratic equation calculator calculates it.




We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 1 comment:
#
Dr Math
that's very mind blowing

avatar









Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2   video3

Next similar math problems:

  • Sphere in cone
    sphere-in-cone A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
  • Cone
    diag22 Into rotating cone with dimensions r = 8 cm and h = 8 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.
  • Cube in sphere
    sphere4 The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
  • Cuboid
    cuboid Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm3. Calculate the length of the other edges.
  • Secret treasure
    max_cylinder_pyramid 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. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
  • 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?
  • Body diagonal
    space_diagonal Calculate the length of the body diagonal of a block with dimensions: a = 20 cm, b = 30 cm, c = 15 cm.
  • Tangent spheres
    tangent_spheres A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and
  • Two balls
    balls-inside-cylinder Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
  • Truncated cone 5
    truncated_cone The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone?
  • Ratio of edges
    diagonal_2 The dimensions of the cuboid are in a ratio 3: 1: 2. The body diagonal has a length of 28 cm. Find the volume of a cuboid.
  • 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.
  • Cube and sphere
    gule_1 Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
  • The diagram 2
    cone The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
  • Solid cuboid
    cuboid_18 A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
  • Cone
    r_h_cone Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
  • Maximum of volume
    kuzel2 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?