Spherical cap

From the sphere of radius 11 was truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere?

Correct answer:

x =  18.2569 %

Step-by-step explanation:

r=11 cm v=6 cm  ρ2=r2(rv)2  ρ=r2(rv)2=112(116)2=4 6 cm9.798 cm  V1=π6 v (3 ρ2+v2)=3.14166 6 (3 9.7982+62)1017.876 cm3  V2=43 π r3=43 3.1416 1135575.2798 cm3  x=100 V1V2=100 1017.8765575.2798=18.2569%

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


Tips to related online calculators
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
Tip: Our volume units converter will help you with the conversion of volume units.
Pythagorean theorem is the base for the right triangle calculator.

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

Related math problems and questions:

  • Spherical cap
    gulovy_odsek Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
  • Sphere - parts
    odsek_vusek Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
  • Spherical cap
    Spherical_cap The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
  • Spherical segment
    circular_segment_1 The spherical segment with height h=1 has a volume V=223. Calculate the radius of the sphere of which is cut this segment.
  • Sphere cut
    odsek_gule A sphere segment is cut off from a sphere k with radius r = 1. The volume of the sphere inscribed in this segment is equal to 1/6 of the segment's volume. What is the distance of the cutting plane from the center of the sphere?
  • Stadium
    sphere_segment A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
  • Spherical cap 4
    spherical cap What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
  • Above Earth
    aboveEarth To what height must a boy be raised above the earth to see one-fifth of its surface.
  • Sphere parts, segment
    gulovy_odsek A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. .What are the volume of the segment and the surface of the segment?
  • Spherical tank
    spherical-tanks The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?
  • A spherical segment
    Spherical_sector A spherical section whose axial section has an angle of j = 120° in the center of the sphere is part of a sphere with a radius r = 10 cm. Calculate the cut surface.
  • Elevation
    horizon_diagram What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
  • Spherical cap
    koule2 What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
  • Cube in a sphere
    cube_in_sphere_1 The cube is inscribed in a sphere with a volume 7253 cm3. Determine the length of the edges of a cube.
  • The roof
    odsek The roof has the shape of a spherical canopy with a base diameter of 8 m and a height of 2 m, calculate the area of the foil with which the roof is covered, when we calculate 13% for waste and residues.
  • 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.
  • Spherical section cut
    gulovy_odsek Find the volume of a spherical section if the radius of its base is 10 cm and the magnitude of the central angle ω = 120 degrees.