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Volume of a Sphere formula = 4/3 * Πr^{3}h

The volume of a sphere measures the space it occupies, crucial in geometry, physics, and engineering.

Enter the sphere's radius to calculate its volume accurately and efficiently.

The formula for calculating the volume of a sphere is:

\[ \text{Volume} = \frac{4}{3} \pi r^3 \]

where \( r \) is the radius of the sphere.

From educational purposes to scientific research and engineering design, this calculator is widely applicable.

**How is the volume of a sphere calculated?**

The volume is \( \frac{4}{3} \pi r^3 \), with \( r \) being the radius.

**Why is the volume formula \(\frac{4}{3}\pi r^3\)?**

This formula is derived from mathematical principles and integration used to calculate the volume enclosed by a sphere.

**What is the volume of a sphere with a 2 cm radius?**

To find the volume, apply the formula with \( r = 2 \) cm: \( \text{Volume} = \frac{4}{3} \pi (2)^3 \).

**What is the equation of a sphere?**

The standard equation for a sphere centered at the origin is \( x^2 + y^2 + z^2 = r^2 \), where \( r \) is the radius.

**How do you solve for volume?**

To solve for volume, especially for a sphere, use the formula \( \text{Volume} = \frac{4}{3} \pi r^3 \) with the given radius.

**How did Archimedes find the volume of a sphere?**

Archimedes used a method of exhaustion, comparing the sphere to a known volume like a cylinder to determine its volume.

**Why is the volume of a sphere \(\frac{4}{3}\) pi \(r^3\)?**

This formula results from integrating the area of circular slices of the sphere, summing up to the total volume.

**What is the volume of a 7.5 cm radius sphere?**

Apply the sphere volume formula with \( r = 7.5 \) cm to find the volume.

**What is the volume of a sphere at 154 cm square?**

If you mean a sphere with a surface area of 154 cm², use the surface area formula to first find the radius, then calculate the volume.

**Why is the volume of a sphere 2/3 the volume of its circumscribing cylinder?**

This relationship was famously proven by Archimedes, showing the sphere's volume is two-thirds that of the cylinder enclosing it.