Practice problems of the spherical cap

Direction: Solve each problem carefully and show your solution in each item.

Number of problems found: 38

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.
Spherical cap 4
What is the surface area of a spherical cap, the base diameter of 20 m, and the height of 2.5 m? Calculate using the formula.
Tropical, mild and arctic
How many percent of the Earth's surface lies in the tropical, mild, and arctic ranges? The border between the ranges is the parallel 23°27' and 66°33'.
MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and 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 ball's surface was 8 cm. Find the diameter of John's ball.
Spherical tank
The water tower tank is a sphere with a radius of 35ft. If the tank is filled to one-quarter full, what is the height of the water?
What percentage
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km.
Float boya
A 0.5-meter spherical float is 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 saltwater weighs 1027 kg/m³.
Felix
Calculate how much land Felix Baumgartner saw after jumping from 36 km above the ground. The radius of the Earth is R = 6378 km.
Elevation
What must be an observer's elevation so that he may see an object on the Earth 536 km away? Assume the Earth to be a smooth sphere with a radius 6378.1 km.
Intersection 40981
The intersection of a plane is 2 cm from the sphere's center, and this sphere is a circle whose radius is 6 cm. Calculate the surface area and volume of the sphere.
Tropics and polar zones
What percentage of the Earth's surface lies in the tropical, temperate, and polar zone? Tropics border individual zones at 23°27' and polar circles at 66°33'.
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.
Above Earth
To what height must a boy be raised above the earth to see one-fifth of its surface?
Sphere - parts
Calculate the area of a spherical cap, which is part of an area with a base radius ρ = 10 cm and a height v = 3.4 cm.
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 cap
From the sphere with a radius of 11 was a truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere?
Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high does he fly?
Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface?
Spherical cap
What is the surface area of a spherical cap, the base diameter 23 m, and height 3 m?
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

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