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Volume of a Sphere With Diameter 10

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Scale: 10 cm
Computed Sphere Volume
523.60 cm³
Surface Area: 314.16 cm² Circumference: 31.42 cm Diameter: 10.00 cm
Fluid Equivalents: 0.52 L 0.14 gal

Formula & Variables

V = ⁴⁄₃ π r³
V = volume of sphere
r = radius of sphere
π ≈ 3.1416 (approx)

Example

Radius = 5 cm
V = ⁴⁄₃ × 3.1416 × 5³
V = ⁴⁄₃ × 3.1416 × 125
V = 523.60 cm³
Also learn about: Sphere Surface Area Sphere Radius Calculator Sphere Diameter Calculator

Worked Solution: Volume of a Sphere with Diameter 10

When given the diameter of a sphere instead of the radius, the most critical first step is to halve the diameter to obtain the radius: r = d / 2 = 10 / 2 = 5.

⚡ Why Dividing by 2 First is Crucial:

Cubing the diameter directly ($10^3$) without dividing by 2 will result in an answer exactly 8 times too large (\(2^3 = 8\))! Alternatively, use the direct diameter formula: V = ¹⁄₆πd³.

Step-by-Step Calculation

Step Action Formula & Working Result
Step 1 Calculate radius from diameter r = d ÷ 2 = 10 ÷ 2 5
Step 2 Cube the radius (5)³ = 5 × 5 × 5 125
Step 3 Apply V = ⁴⁄₃ × π × r³ ⁴⁄₃ × 3.14159 × 125 523.60
Alternative Direct diameter formula: V = ¹⁄₆πd³ ¹⁄₆ × 3.14159 × 1000 523.60
Frequently Asked Questions

Common Questions About Volume of a Sphere With Diameter 10

Simply enter your known measurements into the input boxes above. Select your preferred measurement unit and decimal precision. The calculator updates and outputs exact step-by-step arithmetic proofs in real time.
The radius (r) is the distance from the center to any point on the outer surface. The diameter (d) is the total straight distance across the shape through its center (d = 2r).
The factor of 4/3 comes from the integration of circular cross-sectional disks from -r to +r, or from Archimedes proof demonstrating that a sphere has exactly two-thirds the volume of its circumscribed cylinder.
Yes! Click the 📋 Copy button on the result box to copy formatted mathematical output with units, or click 🔗 Share to copy a shareable web link.
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