Volume & Surface Area: Volume of a Sphere

Learn how to calculate the volume of spheres, spherical shells, and volume ratios with cubes. Practice exercises with step-by-step solutions.

Practice

📖 Learning Guide

A sphere is a perfectly round 3D shape, where every point on its surface is exactly the same distance (the radius

r

) from its center. Its volume represents the total 3D space contained inside the sphere. It is calculated using the radius

r

Sphere

A sphere is a perfectly round three-dimensional solid where every point on the surface is equidistant from the center.

Volume of a Sphere

V = \frac{4}{3} \pi r^3

2. Spherical Shells

A spherical shell is the region between two concentric spheres (a larger outer sphere and a smaller inner sphere). You can think of it as a hollow sphere or a sphere layer. Its volume is found by subtracting the volume of the inner sphere from the volume of the outer sphere:

Spherical Shell

A spherical shell is a three-dimensional solid bounded by two concentric spheres of different radii.

Volume of a Spherical Shell

V = \frac{4}{3} \pi \left(R^3 - r^3\right)

Calculated using outer radius

R

and inner radius

r

Learning Topics

Frequently Asked Questions

What is volume?

Volume is the amount of three-dimensional space occupied by an object. It is measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

How do you calculate the volume of a box?

The volume of a box (rectangular prism) is calculated by multiplying its length, width, and height: V = l × w × h.