Sphere Problems

Number of problems found: 109

  • 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 volume of the segment. What is the distance of the cutting plane from the center of the sphere?
  • Sphere area
    sphere A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.
  • Sphere cuts
    sphere_cut At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
  • Cube in sphere
    sphere4 The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
  • Sphere
    cone_sphere_center_1 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.
  • Sphere radius
    SpheresDiff The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
  • Cube and sphere
    gule_1 Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
  • Sphere vs cube
    koule_krychle How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
  • Sphere growth
    sphere How many times grow volume of sphere if diameter rises 10×?
  • Gas sphere
    sphere_tank The gas tank has the shape of a sphere with a diameter of 14 m. How many m3 of gas will fit in it?
  • Sphere VS
    gule Find the surface and volume of a sphere that has a radius of 2 dm.
  • Sphere fall
    sphere How many percent fall volume of a sphere if diameter decrease 3×?
  • Hollow sphere
    sphere_2 The steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and the density of steel is 7850 kg/m3
  • Volume of sphere
    sphere_in_cube How many times does the volume of a sphere increase if its radius increases 2 ×?
  • Cube into sphere
    cube_sphere_in The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
  • Inscribed sphere
    cubes2_7 How many percent of the cube volume takes the sphere inscribed into it?
  • Cube, cuboid, and sphere
    cubes3_8 Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. At what rate are the volumes of cube, cuboid, and sphere?
  • Sphere from tree points
    sphere2_1 Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
  • Cube in ball
    sphere2 Cube is inscribed into the sphere of radius 181 dm. How many percent is the volume of cube of the volume of the sphere?
  • Sphere A2V
    sphere3 The surface of the sphere is 241 mm2. What is its volume?

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...
We encourage you to watch this tutorial video on this topic.



See also more information on Wikipedia.