Right triangle + sphere - practice problems - last page
Number of problems found: 39
- 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. - Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high does he fly? - Cube and sphere
A cube with a surface area of 150 cm² is described sphere. What is a sphere surface? - 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 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. - Sphere cuts
At what distance from the center intersects the sphere with radius R = 91 plane if the cut area and area of the main sphere circle are in ratio 3/6? - The spacecraft
The spacecraft spotted a radar device at an 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 considere - Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes. - Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
- 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? - 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. - Big Earth
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. - Horizon
The top of a lighthouse is 19 m above the sea. How far away is an object just "on the horizon"? [Assume the Earth is a sphere of radius 6378.1 km.] - 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.
- Spherical cap
Calculate the volume of the spherical cap and the areas of the spherical canopy if r = 5 cm (radius of the sphere), ρ = 4 cm (radius of the circle of the cap). - 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. - 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. - 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?
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