# Sphere + body volume - 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. 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?
5. 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.
6. 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.
7. 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.
8. 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?
9. 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
10. Sphere in cone
A sphere of radius 3 cm desribe cone with minimum volume. Determine cone dimensions.
11. Sphere A2V
Surface of the sphere is 241 mm2. What is its volume?
12. 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.
13. 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
14. 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.
15. 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.
16. Shots
5500 lead shots with diameter 4 mm is decanted into a ball. What is it diameter?
17. Sphere growth
How many times grow volume of sphere if diameter rises 10×?
18. Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
19. Chemical parison
The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface?
20. Sphere
Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.

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