Spherical segment
The spherical segment with height h=2 has a volume of V=112. Calculate the radius of the sphere which is cut in this segment.
Correct answer:
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Dr. Math
To find the radius R of the sphere from which a spherical segment of height h = 2 and volume V = 112 is cut, we can use the formula for the volume of a spherical segment:
Given:
- V = 112
- h = 2
Substitute the known values into the formula:
Simplify the equation - thus, the radius R of the sphere is:
This is the exact form of the radius. If a numerical approximation is needed, you can substitute π ≈ 3.1416 :
So, the radius of the sphere is approximately 9.58 units.
V = π h2 (3R - h)/3
Given:
- V = 112
- h = 2
Substitute the known values into the formula:
112 = π (2)2 (3R - 2)/3
Simplify the equation - thus, the radius R of the sphere is:
R = 28/π + 2/3
This is the exact form of the radius. If a numerical approximation is needed, you can substitute π ≈ 3.1416 :
R ≈ 28/3.1416 + 2/3 ≈ 8.9127 + 0.6667 ≈ 9.5794
So, the radius of the sphere is approximately 9.58 units.
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You need to know the following knowledge to solve this word math problem:
- algebra
- expression of a variable from the formula
- solid geometry
- sphere
- spherical cap
- planimetrics
- circular segment
Units of physical quantities:
Grade of the word problem:
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