The volume of a sphere is an important concept in mathematics, especially in geometry and real-life measurement problems. It helps us understand how much three-dimensional space is occupied by spherical objects like balls, globes, bubbles, tanks, or even planets. Students preparing for exams such as CUET, SSC, Banking, and JEE often come across this formula because it forms the basis of many capacity-related questions.
Understanding the formula makes it easy to solve questions quickly and accurately.
Volume of a Sphere Formula Overview
| Formula | Variables & Meaning | When It Is Used |
|---|---|---|
| V = (4/3) × π × r³ | r = radius, π = 3.1416 | Used to find how much space a spherical object contains |
What is Volume of a Sphere?
The volume of a sphere is the amount of three-dimensional space enclosed by its curved surface. In mathematical terms, it represents the total capacity inside a sphere. The formula V = (4/3)πr³ shows that the volume depends on the radius raised to the power of three. This means even a small increase in radius causes a large increase in volume.
The term r³ means multiplying the radius by itself three times. The constant (4/3)π(4/3)π(4/3)π comes from the process of integrating circular slices that make up the entire sphere. To use the formula, simply measure the radius (half the diameter), cube it, multiply by π, and finally multiply by 4/3.
This formula is widely used to calculate the air capacity of footballs, design spherical tanks, understand planetary sizes, and solve geometry questions in exams like CUET, SSC, JEE, and Banking.
Examples to Calculate Volume of a Sphere
Example 1: Volume of a sphere with radius 7 cm
Given: r = 7 cm
Step 1: V = (4/3) × π × r³
Step 2: V = (4/3) × 3.1416 × 7³
Step 3: V = 4.1888 × 343
Volume = 1436.76 cm³
Answer: The volume of the sphere is 1436.76 cm³.
Example 2: Volume of a sphere with a diameter of 12 m
Given: Diameter = 12 m → r = 6 m
Step 1: V = (4/3) × π × r³
Step 2: V = (4/3) × 3.1416 × 6³
Step 3: V = 4.1888 × 216
Volume = 904.78 m³
Answer: The volume of the sphere is 904.78 m³.
FAQs About Volume of a Sphere Formula
Q1. What does r³ mean in the formula?
It means radius × radius × radius. It represents the three-dimensional measure of the sphere.
Q2. Can I use 22/7 instead of π?
Yes, π = 22/7 can be used for easy and quick calculations.
Q3. Is volume always measured in cubic units?
Yes, the unit will always be in cubic form, such as cm³, m³, or mm³.
Q4. How is volume different from surface area?
Surface area measures the outer covering of a sphere, while volume measures the internal space it occupies.
Q5. Where is the sphere volume formula used in real life?
It is used in calculating the capacity of spherical balloons, balls, bubbles, tanks, and even planets.
Q6. In which exams is the sphere volume formula important?
Important for CUET, SSC, JEE, Banking exams, and all school-level maths tests.