# Sphere - problems

1. Cube in a sphere The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
2. Cubes One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
3. Sphere Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
4. 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. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
5. Spherical cap From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere?
6. Earth parallel Earth's radius is 6374 km long. Calculate the length parallel of latitude 70°.
7. 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.
8. Sphere slices Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
9. Hollow sphere Calculate the weight of a hollow tungsten sphere (density 19.3 g/cm3), if the inner diameter is 14 cm and wall thickness is 3 mm.
10. Balls Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
11. Cube in ball Cube is inscribed into sphere of radius 241 cm. How many percent is the volume of cube of the volume of sphere?
12. Balls Ping pong balls have a diameter of approximately 4.6 cm. They are sold in boxes of 4 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled w
13. Sphere in cone A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
14. Sphere A2V Surface of the sphere is 241 mm2. What is its volume?
15. 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.
16. Hollow sphere Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
17. Spherical segment Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment.
18. Sphere and cone Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
19. 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.
20. Plasticine ball Plasticine balls have radius r1=85 cm, r2=60 mm, r3=59 cm, r4=86 cm, r5=20 cm, r6=76 mm, r7=81 mm, r8=25 mm, r9=19 mm, r10=14 cm. For these balls.

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