Right triangle + sphere - math problems

Number of problems found: 32

Sphere cuts
At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
Cube and sphere
Cube with the surface area 150 cm² is described sphere. What is sphere surface?
Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a
Sphere equation
Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1).
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
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?
A spherical segment
A spherical 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.
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
Horizon
The top of a lighthouse is 19 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.]
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.
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?
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.
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
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.
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.
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 257 mm².
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
Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.
Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface?