Body volume of a sphere problems

Number of problems found: 57

  • Clay balls
    balls2 How many clay balls with a radius of 1 cm can be made from a ball of clay with a radius of 8 cm?
  • Volume ratio
    inside_cone Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone.
  • Hemisphere cut
    odsek_gule Calculate the volume of the spherical layer that remains from the hemisphere after the 3 cm section is cut. The height of the hemisphere is 10 cm.
  • Kostka
    sphere_in_cube Kostka je vepsána do koule o poloměru r = 6 cm. Kolik procent tvoří objem kostky z objemu koule?
  • The water tank
    hydroglobus The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank, if we paint with 1 kg of paint 10 m2?
  • The prison ball
    prisonBall Calculate the density of the material that the prison ball is made from if you know its diameter is 15cm and its weight is approximately 2.3kg. With the help of mathematical-physicochemical tables estimate what material the ball is made from.
  • Eight
    sphere_in_cube Eight small Christmas balls with a radius of 1 cm have the same volume as one large Christmas ball. What has a bigger surface: eight small balls, or one big ball?
  • Wall thickness
    sphere_Nickel The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
  • Volume of ball
    ball1_5 Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π
  • Hemispherical hollow
    odsek The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
  • The ball
    sphere4 The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
  • Hemisphere - roof
    kupola The shape of the observatory dome is close to the hemisphere. Its outer diameter is 11 m. How many kilograms of paint and how many liters of paint is used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of paint will paint an a
  • Sphere floating
    SpheresDiff Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )
  • Alien ship
    cube_in_sphere The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large
  • 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?
  • 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.
  • 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?
  • What is bigger?
    ball_f Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm?
  • The hemisphere
    naklon_koule The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
  • Iron ball
    damper_sphere The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm3.

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...