Finding the volume and surface area of a sphere
A sphere is the three-dimensional version of a circle
In this lesson we’ll look at the volume and surface area of spheres. A sphere is a perfectly round ball; it’s the three-dimensional version of a circle.
Volume and surface area
The volume of a sphere is given by
???V=\frac{4}{3}\pi r^3???
The symbol ???\pi??? is used for exact answers and ???\pi \approx 3.14??? is used for approximate answers.
The surface area of a sphere is given by
???S=4\pi r^2???
How to find the volume and surface area of a sphere
Take the course
Want to learn more about Geometry? I have a step-by-step course for that. :)
Using the formula for the surface area of a sphere
Example
What is the surface area of the sphere?
Use the formula for surface area, then plug in the value for the radius.
???S=4\pi r^2???
???S=4\pi (5)^2???
???S=100\pi \text{ cm}^2???
Let’s try one with volume.
Example
What is the volume of a sphere with a diameter of ???50\text{ cm}????
The formula for volume is
???V=\frac{4}{3}\pi r^3???
We’re given the diameter, so we need to divide by ???2??? to get the radius.
???r=\frac{d}{2}???
???r=\frac{50\text{ cm}}{2}???
???r=25\text{ cm}???
Plugging into the formula for volume, we get
???V=\frac{4}{3}(3.14){{(25)}^{3}}???
???V=\frac{4}{3}(3.14){{25}^{3}}???
???V=\frac{4}{3}\cdot 3.14\cdot 15,625???
???V\approx 65,416.67\text{ cm}???