How to Calculate Volume of a Ball

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Sphere Volume Calculator

Radius (r) Diameter (d)
Centimeters (cm) Meters (m) Inches (in) Feet (ft)

Results:

function toggleInputs() { var type = document.getElementById("calc_type").value; var radiusGroup = document.getElementById("radius_group"); var diameterGroup = document.getElementById("diameter_group"); if (type === "radius") { radiusGroup.style.display = "block"; diameterGroup.style.display = "none"; } else { radiusGroup.style.display = "none"; diameterGroup.style.display = "block"; } } function performVolumeCalculation() { var type = document.getElementById("calc_type").value; var unit = document.getElementById("unit_measure").value; var r = 0; var volume = 0; if (type === "radius") { r = parseFloat(document.getElementById("ball_radius").value); } else { var d = parseFloat(document.getElementById("ball_diameter").value); r = d / 2; } if (isNaN(r) || r <= 0) { alert("Please enter a valid positive number for the measurement."); return; } // Formula: V = (4/3) * PI * r^3 volume = (4/3) * Math.PI * Math.pow(r, 3); var resultBox = document.getElementById("volume_result_box"); var volumeOutput = document.getElementById("volume_output"); var formulaDisplay = document.getElementById("formula_display"); resultBox.style.display = "block"; volumeOutput.innerHTML = volume.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 4}) + " " + unit + "³"; formulaDisplay.innerHTML = "Calculated using: V = 4/3 × π × " + r.toFixed(2) + "³"; }

How to Calculate the Volume of a Ball

In geometry, a ball is formally known as a sphere. Calculating the volume of a sphere allows you to determine how much space is contained within its perfectly round boundary. This is useful for everything from physics experiments to calculating how much air is inside a basketball or how much material is needed to manufacture a steel bearing.

The Sphere Volume Formula

To find the volume (V), you only need to know the radius (r) of the ball. The radius is the distance from the exact center of the sphere to any point on its surface. The mathematical formula is:

V = 4/3 × π × r³

Where:

  • V = Volume
  • π (Pi) ≈ 3.14159
  • r = Radius of the sphere

Step-by-Step Calculation Guide

  1. Find the Radius: If you know the diameter (the distance across the widest part of the ball), simply divide it by 2. For example, if a ball is 10cm wide, the radius is 5cm.
  2. Cube the Radius: Multiply the radius by itself twice (r × r × r). If the radius is 5, then 5³ = 5 × 5 × 5 = 125.
  3. Multiply by Pi: Take that result and multiply it by π (approximately 3.14159). 125 × 3.14159 ≈ 392.70.
  4. Multiply by 4/3: Finally, multiply by 4 and divide by 3. 392.70 × 4 / 3 ≈ 523.60.

Practical Example: Measuring a Soccer Ball

A standard size 5 soccer ball has a radius of approximately 11 cm. Let's calculate its volume:

  1. Radius (r): 11 cm
  2. r³: 11 × 11 × 11 = 1,331
  3. V = 4/3 × π × 1,331
  4. V ≈ 1.333 × 3.14159 × 1,331
  5. V ≈ 5,575.28 cm³

This means a soccer ball holds roughly 5.57 liters of air!

Common Units of Volume

When you calculate the volume of a ball, the units are always "cubed." Common units include:

  • Cubic centimeters (cm³) – often used for small balls or liquid displacement.
  • Cubic inches (in³) – common in US imperial measurements.
  • Cubic meters (m³) – used for very large spherical structures like gas tanks or planets.

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