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 ) from its center. Its volume represents the total 3D space contained inside the sphere. It is calculated using the radius :
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:
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.
What is the surface area of a shape?
Surface area is the total area of all the exterior faces of a 3D shape. It represents how many square units are needed to completely cover the outside of the shape without any overlaps.
How do you calculate the volume of a sphere?
The volume of a sphere is calculated using the formula: , where is the radius of the sphere.