Pythagorean theorem + sphere - math problems

Number of problems found: 33

Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
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 and sphere
Cube with the surface area 150 cm² is described sphere. What is sphere surface?
Sphere vs cube
How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
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?
Sphere slices
Calculate the volume and surface of a sphere if the radii of parallel cut r₁=31 cm, r₂=92 cm, and its distance v=25 cm.
Spherical cap
From the sphere of radius 11 was truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere?
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.
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).
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?
Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube.
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.]
Cube from sphere
What largest surface area (in cm²) can have a cube that was cut out of a sphere with radius 43 cm?
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
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
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.
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.
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.
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