Spherical Sector Volume
Calculator
Results
- Volume
- 837.75804
- Curved surface area
- 251.327412
- Total surface area
- 502.654824
Results
| Volume | 837.75804 |
| Curved surface area | 251.327412 |
| Total surface area | 502.654824 |
formula-map diagram
- Volume
- 837.75804
- Curved surface area
- 251.327412
- Total surface area
- 502.654824
Formula map
Formula
V = (2/3) × π × R² × h= 837.75804095728
Note
Simplified model: these are the exact results of the stated idealised geometric formulas, assuming perfect shapes, exact inputs and consistent units. Real measurements carry error, and results such as the cyclic-quadrilateral area only hold when the figure truly satisfies the stated condition. Verify independently before relying on these figures.
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See all →Frequently asked questions
What is a spherical sector, and how is it different from a spherical cap?+
A spherical sector is a cone-like 'ice cream cone' shape formed by combining a spherical cap with the cone connecting the cap's edge to the sphere's center, whereas a spherical cap is just the curved cap portion alone. The sector includes the extra conical volume beneath the cap.
What is the formula for the volume of a spherical sector?+
Volume is V = (2πr²h)/3, where r is the sphere's radius and h is the height of the spherical cap portion. Despite the more complex shape, the formula is actually simpler in form than the cap formula alone.
What happens to the spherical sector formula if the cap height equals the full diameter?+
When h = 2r, the formula gives V = (2πr²)(2r)/3 = (4/3)πr³, exactly the full sphere's volume. This makes sense because a cap spanning the whole sphere leaves no room for a separate cone, so the sector becomes the entire sphere.
Why is the spherical sector shape relevant to real objects?+
The spherical sector shape appears in ice-cream-cone-style containers, certain lamp shades, and mathematical modeling of sectors cut from spherical tanks. It's a natural shape whenever a cone-and-cap combination bounded by the sphere's center is needed.
Does this formula require knowing the cone's separate volume and adding it to the cap's volume?+
No, that's the more laborious approach; the combined formula V = (2πr²h)/3 already accounts for both pieces together in a single simplified expression. It was derived by adding the cap and cone volume formulas and simplifying algebraically, so you don't need to compute them separately.