Right triangle + sphere - practice problems

Number of problems found: 34

Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
Billiard balls
A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original.
The spacecraft
The spacecraft spotted a radar device at altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is considered a
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.
Moon
We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
Cubes
One cube is an inscribed sphere and the other one described. Calculate the difference of volumes of cubes, if the difference of surfaces in 231 cm².
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'.
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 the radius R = 6370 km
Rotation of the Earth
Calculate the circumferential speed of the Earth's surface at a latitude of 61°. Consider a globe with a radius of 6378 km.
Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. In order not to attract attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal?
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?
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?
Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in a corner of a room. The spheres are each tangent to the walls and floor and
Sphere and cone
Within the sphere of radius G = 33 cm inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone?
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 the spherical cap was cut.
Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
Metal balls
Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level?
Elevation
What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.

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