Volume ratio

Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone.

Correct answer:

r =  8:1

Step-by-step explanation:

a=1  r1=3/3 a=3/3 10.5774 r2=3/6 a=3/6 10.2887  V1=43 π r13=43 3.1416 0.577430.8061 V2=43 π r23=43 3.1416 0.288730.1008  r=V1V2=0.80610.10088=8:1



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






avatar




Tips to related online calculators
Check out our ratio calculator.
Tip: Our volume units converter will help you with the conversion of volume units.

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


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

Related math problems and questions:

  • Equilateral cylinder
    sphere_in_cylinder A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
  • Inscribed sphere
    cubes2 How many percent of the cube volume takes the sphere inscribed into it?
  • Truncated cone 6
    frustum-of-a-right-circular-cone Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
  • Inscribed sphere
    ball-in-cube How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?
  • Rotating cone
    kuzel Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
  • Sphere in cone
    sphere_in_cone A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
  • Balls
    balls Ping pong balls have a diameter of approximately 5.1 cm. It sold in boxes of 10 pieces: each box has a cuboid shape with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled with balls.
  • Axial section of the cone
    rez_kuzel The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
  • 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.
  • 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?
  • The rotating
    kuzel3 The rotating cone has a height of 0.9 m and the diameter of the base is 7.2 dm. Calculate the surface of the cone. (Hint: use Pythagorean theorem for a side of cone)
  • Axial cut
    Kuzel The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
  • Sphere
    cone_sphere_center Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.
  • Rotating cone
    kuzel2 The rotating cone has a base diameter of 18 dm and a height of 12 dm. Calculate the volume V.
  • The funnel
    kuzel_rs The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel.
  • Axial section
    cone2 The axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
  • Sphere in cone
    sphere-in-cone A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions.