Volume & Surface Area: Surface Area of a Sphere

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

Practice

📖 Learning Guide

The surface area of a sphere represents the total area of the outside boundary of 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.

Surface Area of a Sphere

A = 4 \pi r^2

2. Spherical Shell Surface Area

For a hollow spherical shell, the total surface area consists of both the outer surface area and the inner surface area. It is found by adding them together:

Spherical Shell

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

Surface Area of a Spherical Shell

A = 4 \pi \left(R^2 + r^2\right)

Calculated as the sum of outer and inner surface areas using outer radius

R

and inner radius

r

Learning Topics

Frequently Asked Questions

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 surface area of a sphere?

The surface area of a sphere is calculated using the formula:

A = 4 \pi r^2

, where

r

is the radius of the sphere.