Spherical cap - problems
- 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. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
- Spherical cap
From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere?
- Spherical segment
Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment.
What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
Calculate how much land saw Felix Baumgartner after jump from 32 km above ground. The radius of the Earth is R = 6378 km.
- Sphere - parts
Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
- Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
- Spherical cap
What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
- 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/m
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.