Practice problems of the spherical cap

Number of problems found: 34

Sphere submerged in the cone
A right circular cone with a top width of 24 cm and an altitude of 8 cm is filled with water. A spherical steel ball with a radius of 3.0cm is submerged in the cone. Find the volume of water below the sphere.
Sphere cut
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?
Spherical segment
Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.
Hemisphere cut
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.
Hemisphere - roof
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
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 t
The observatory
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?
Spherical tank
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
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
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?
Gasholder
The gasholder has spherical shape with a diameter 20 m. How many m³ can hold in?
Float boya
A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/
MO SK/CZ Z9–I–3
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.
Tropics and polar zones
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'.
Stadium
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 section cut
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.
The hemisphere
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
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.
A spherical segment
The aspherical 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.
Sphere parts, segment
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?

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.