# Sphere - problems - page 3

1. 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?
2. Cube from sphere
What largest surface area (in cm2) can have a cube that was cut out of a sphere with radius 43 cm?
3. Average speed
What is the average speed you have to move the way around the world in 80 days? (Path along the equator, round to km/h).
4. Earth's surface
The greater part of the earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land?
5. Float boya
A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/m
6. Spheres in sphere
How many spheres with a radius of 15 cm can fits into the larger sphere with a radius of 150 cm?
7. Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
8. Billiard balls
A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
9. Hollow sphere
The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?
10. Cube in sphere
The sphere is inscribed cube with edge 8 cm. Find the radius of the sphere.
A domed stadium is in the shape of spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the height of the dome at its centre to the nearest tenth of a meter.
12. Fit ball
What is the size of the surface of Gymball (FIT - ball) with a diameter of 65 cm?
13. Inscribed sphere
How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?
The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm.
15. Inscribed sphere
How many percents of the cube volume takes the sphere inscribed into it?
16. 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).
17. Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
18. Cube, cuboid, and sphere
Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
19. 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
20. Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent was the waste.

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