Spherical cap - practice for 14 year olds
Number of problems found: 25
- 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. - 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. - 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. - 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? - 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 cap
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 we cut the spherical cap. - Spherical segment
Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, and the upper base is 60 cm. - Calculate 81034
Calculate the volume of the spherical segment and the surface area of the canopy if the radius of the sphere is r=5cm and the radius of the circular base of the segment ρ=4cm. - 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? - Spherical segment
The spherical segment with height h=2 has a volume of V=112. Calculate the radius of the sphere of which is cut this segment.
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