Sphere + Pythagorean theorem - practice problems
Number of problems found: 47
- 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 slices
Calculate the volume and surface of a sphere if the radii of a parallel cut r1=32 cm, r2=47 cm, and its distance v=21 cm. - 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.] - 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).
- 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? - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Cube from sphere
What largest surface area (in cm²) can have a cube that we cut out of a sphere with a radius 26 cm? - Billiard balls
A layer of ivory billiard balls radius of 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to everyone adjacent to it. In the spaces between sets of 4 adjacent balls, other balls rest, equal in size to the original. - 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 the corner of a room. The spheres are each tangent to the walls and floor an
- 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. - 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. - Cube in sphere
The cube is inscribed in a sphere with a radius r = 6 cm. What percentage is the cube's volume from the ball's volume? - Identical 35961
Nine identical spheres are stacked in the cube to fill the volume of the cube as much as possible. What part of the volume will the cube fill? - 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?
- Inscribed 81949
A cube is inscribed in a sphere with a radius of 27 cm. Calculate its volume and surface area. - Sphere vs cube
How much % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere? - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Cube and sphere
A cube with a surface area of 150 cm² is described sphere. What is a sphere surface? - Cube in sphere
The sphere is an inscribed cube with an edge of 8 cm. Find the sphere's radius.
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