Step-by-Step Tutorials

Sphere Volume Solved Examples

Explore 20 fully worked mathematics problems with clear algebraic steps, exact Pi values, and decimal answers.

Example 1: Radius = 3 cm V ≈ 113.10 cm³

Given: Radius r = 3 cm, π ≈ 3.14159

1. Calculate r³: 3³ = 27
2. Apply formula: V = 4/3 × π × 27
3. Exact Answer: 36π cm³
4. Decimal Answer: 36 × 3.14159 = 113.10 cm³
Example 2: Radius = 5 cm V ≈ 523.60 cm³

Given: Radius r = 5 cm

1. Calculate r³: 5³ = 125
2. Apply formula: V = 4/3 × π × 125 = 500π/3
3. Decimal Answer: (500 / 3) × 3.14159 = 523.60 cm³
Example 3: Diameter = 10 cm d = 10 cm → r = 5 cm

Given: Diameter d = 10 cm → Radius r = 10 / 2 = 5 cm

1. Divide diameter by 2: r = 5 cm
2. Apply formula: V = 4/3 × π × 5³ = 523.60 cm³

Directory of All 20 Worked Examples

4.19 units³

Volume of a Sphere With Radius 1

r = 1, V = 4/3 π (1)³ = 4/3 π ≈ 4.19.

View Complete Solution →
33.51 units³

Volume of a Sphere With Radius 2

r = 2, V = 4/3 π (8) = 32π/3 ≈ 33.51.

View Complete Solution →
113.10 units³

Volume of a Sphere With Radius 3

r = 3, V = 4/3 π (27) = 36π ≈ 113.10.

View Complete Solution →
268.08 units³

Volume of a Sphere With Radius 4

r = 4, V = 4/3 π (64) = 256π/3 ≈ 268.08.

View Complete Solution →
523.60 units³

Volume of a Sphere With Radius 5

r = 5, V = 4/3 π (125) = 500π/3 ≈ 523.60.

View Complete Solution →
4,188.79 units³

Volume of a Sphere With Radius 10

r = 10, V = 4/3 π (1000) = 4000π/3 ≈ 4,188.79.

View Complete Solution →
4.19 units³

Volume of a Sphere With Diameter 2

d = 2 → r = 1, V = 4/3 π ≈ 4.19.

View Complete Solution →
33.51 units³

Volume of a Sphere With Diameter 4

d = 4 → r = 2, V = 32π/3 ≈ 33.51.

View Complete Solution →
113.10 units³

Volume of a Sphere With Diameter 6

d = 6 → r = 3, V = 36π ≈ 113.10.

View Complete Solution →
523.60 units³

Volume of a Sphere With Diameter 10

d = 10 → r = 5, V = 500π/3 ≈ 523.60.

View Complete Solution →
Metric cm³

Sphere Volume Example in cm

Worked problem with metric centimeter units and conversion to milliliters.

View Complete Solution →
Metric m³

Sphere Volume Example in m

Large scale problem in cubic meters and conversion to 1,000 Liters.

View Complete Solution →
Imperial in³

Sphere Volume Example in inches

Industrial manufacturing problem calculating cubic inches.

View Complete Solution →
Imperial ft³

Sphere Volume Example in feet

Storage tank problem converting cubic feet into US Gallons.

View Complete Solution →
A = 4πr²

Sphere Surface Area Example

Step-by-step worked example calculating exterior surface area.

View Complete Solution →
r = ³√[(3V)/(4π)]

Sphere Radius From Volume Example

Step-by-step example solving for radius when volume is given.

View Complete Solution →
d = 2r

Sphere Diameter From Volume Example

Worked problem calculating total diameter from given cubic volume.

View Complete Solution →
Applied Math

Sphere Volume Word Problems

Real-world basketball, planets, water droplets, and spherical tanks.

View Complete Solution →
Student Exercises

Sphere Volume Practice Problems

Self-testing homework problems with revealable solution keys.

View Complete Solution →
Full Answer Key

Sphere Volume Examples With Answers

Consolidated reference sheet of 20 solved problems with answers.

View Complete Solution →