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.

Correct answer:

r =  2.67 cm
h =  5.33 cm

Step-by-step explanation:

V=13πr2h x/R=2r/H  r=H2Rx=828x h=2(Rx)=2(8x)  V=13π(828x)22(8x)  V=π82682(8x2x3)  V=π82682(28x3x2) V=0 28x3x2=0 x1=0 283x=0  16=3x  x=5.333 cm r=8285.333=2.67 cm 
h=2(85.333)=5.33 cm

Did you find an error or inaccuracy? Feel free to write us. Thank you!


You need to know the following knowledge to solve this word math problem:

Related math problems and questions:

  • Sphere in cone
    sphere-in-cone A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.
  • 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?
  • Cylindrical container
    valec2 An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
  • Cross-sections of a cone
    kuzel_rezy Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body.
  • Paper box
    box The 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 beside the squares be the largest volume of the box?
  • Max - cone
    cone From the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, 6.2 cm must be produced the greatest cone. a) Calculate cone volume. b) Calculate the waste.
  • Jar
    sklenice From the cylinder shaped jar after tilting spilled water so that the bottom of the jar reaches the water level accurately into half of the base. Height of jar h = 7 cm and a jar diameter D is 12 cm. How to calculate how much water remains in the jar?
  • Largest possible cone
    cone-upside It is necessary to make the largest possible cone from an iron rod in the shape of a prism with dimensions of 5.6 cm, 4.8 cm, 7.2 cm. a) Calculate its volume. b) Calculate the waste.
  • 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?
  • Metal balls
    three_circles_inside_one Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level?
  • Rotating cone
    cone Calculate volume of a rotating cone with base radius r=12 cm and height h=7 cm.
  • 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.
  • The truncated
    truncated_cone The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm and height v = 5 cm. What is the volume of the cone from which the truncated cone originated?
  • Cone
    valec The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
  • Cone in cylinder
    cone_in_cylinder The cylinder is inscribed cone. Determine the ratio of the volume of cone and cylinder. The ratio express as a decimal number and as percentage.
  • Surface area
    cone_slice The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone.
  • Frustrum - volume, area
    frustum-of-a-right-circular-cone Calculate the surface and volume of a truncated rotating cone with base radii of 8 cm and 4 cm, height 5 cm.