# Sphere + expression of a variable from formula - problems

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.
2. Cube in a sphere
The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
3. 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.
4. Sphere A2V
Surface of the sphere is 241 mm2. What is its volume?
5. 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
6. 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.
7. Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
8. Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
9. Moon
We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
10. Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
11. Cube and sphere
Cube with the surface area 150 cm2 is described sphere. What is sphere surface?
12. 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
13. Hollow sphere
The volume of the hollow ball is 3432 cm3. What is its internal radius when the wall thickness is 3 cm?
The surface of the sphere is 60 cm square. Calculate its radius; result round to tenth of cm.
15. 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).
16. Cube into sphere
The cube has brushed a sphere as large as possible. Determine how much percent was the waste.
17. Spherical tank
The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?
18. Pilot
How high is the airplane's pilot to see 0.001 of Earth's surface?

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