Spherical cap Problems

Number of problems found: 30

  • 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.
  • 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?
  • 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 segment
    SphericalSegment Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.
  • Two hemispheres
    hemisphere3 In a wooden hemisphere with a radius r = 1, a hemispherical depression with a radius r/2 was created so that the bases of both hemispheres lie in the same plane. What is the surface of the created body (including the surface of the depression)?
  • 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.
  • Hemisphere cut
    odsek_gule Calculate the spherical layer's volume that remains from the hemisphere after the 3 cm section is cut. The height of the hemisphere is 10 cm.
  • Tropics and polar zones
    circles_on_Earth What percentage of the Earth's surface lies in the tropical, temperate, and polar zone? Individual zones are bordered by tropics 23°27' and polar circles 66°33'.
  • 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 thinner is used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of thinner will paint
  • The cylindrical container
    balls2 The cylindrical container has a base area of 300 cm3 and a height of 10 cm. It is 90% filled with water. We gradually insert metal balls into the water, each with a volume of 20 cm3. After inserting how many balls for the first time does water flow over
  • 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?
  • The roof
    odsek The roof has a spherical canopy with a base diameter of 8 m and a height of 2 m. Calculate the foil area with which the roof is covered when calculating 13% for waste and residues.
  • 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.
  • 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.
  • The observatory
    kupola The dome of the hemisphere-shaped observatory is 5.4 meters high. How many square meters of sheet metal needs to be covered to cover it, and 15 percent must be added to the minimum amount due to joints and waste?
  • Pilot
    aircraft-02 How high is the airplane's pilot to see 0.001 of Earth's surface?
  • 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?
  • Tropical, mild and arctic
    tropic How many percent of the Earth's surface lies in the tropical, mild, and arctic range? The border between the ranges is the parallel 23°27' and 66°33'.
  • 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 hollow's inside diameter is d = 28cm?
  • MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool, and it swam in the water. Its highest point was 2 cm above the surface. The diameter of the circle that marked the water level on the surface of the ball was 8 cm. Find the diameter of John ball.

Do you have an exciting math question or word problem that you can't solve? Ask a question or post 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...