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Introduction

QUICK LINKS


Introduction

Volume and Surface Area of Spheres

INTRO
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Volume tells us the amount of space inside a given 3D shape. Surface area tells us the area of the surface of a 3D shape.
Think of it in terms of an apple. The volume is the total amount of apple, and the surface area is the amount of skin on the apple.
The only thing we need to know in order to get both the surface area and volume is the radius. The radius of a sphere is the distance from the center of the sphere to its surface.Once we know the radius, we can calculate the volume and surface area of a sphere using the following formulas:Try some problems out with our calculator or scroll down to learn more about how to find the volume and surface area of a sphere.
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Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to find the area of triangles and test your understanding.

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CALCULATOR
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Volume and Surface Area of Spheres Calculator

Step 1. Determine if you’re solving for volume (V) or surface area (SA).

An apple's surface area and volume
KEY STEPS
β€”

How to Find the Volume and Surface Area of a Sphere

Step 1. Determine if you’re solving for volume (V) or surface area (SA).

What are you trying to solve for?
We're looking for the volume, or the total amount of space inside the sphere, which is like the total amount of apple.

Step 2. Find the radius of the sphere.

The radius is the distance from the center of the sphere to the surface.

Step 3. Calculate the volume with the radius.

LESSON
β€” Volume of Spheres

Volume of Spheres

Finding the volume of a sphere is like finding the total amount of fruit inside the apple, and the only thing we need to know in order to solve for the volume of a sphere is its radius.Let’s put this formula to use by doing a couple example problems where we solve for the volume of a sphere!

EXAMPLE 1

Let's say we know our sphere has radius . What is the volume?

Step 1. Determine if you’re solving for volume (V) or surface area (SA).

We're looking for the volume, which is the amount of space inside the sphere.
The formula for finding the volume of a sphere is:

Step 2. Find the radius of the sphere.

The radius is given to us and is equal to .

Step 3. Calculate the volume with the radius.

Our answer is .

EXAMPLE 2

Great job! Try one more - say the radius . What is the volume?

Step 1. Determine if you’re solving for volume (V) or surface area (SA).

We're looking for the volume, which is the amount of space inside the sphere.
The formula for finding the volume of a sphere is:

Step 2. Find the radius of the sphere.

The radius is given to us and is equal to .

Step 3. Calculate the volume with the radius.

Our answer is .
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do when we're dealing with the surface area of spheres.
PRACTICE
β€” Volume of Spheres

Practice: Volume of a Sphere

Question 1 of 3: What is the volume of a sphere with ?

Step 1. Determine what you are solving for.

Image of Apple
Finding the volume of a sphere is like finding the total amount of an apple.
Nice! Since we’re solving for volume, which equation should we use?
That's right! The formula for the volume of a sphere is
Looks like we’re ready for the next step!

Step 2. Find the radius of the sphere.

What is the sphere's radius?
Nice work! Now plug in:

Step 3. Calculate the volume with the radius.

Awesome! The volume of the sphere is Β .

LESSON
β€” Surface Area of Spheres

Surface Area of Spheres

Finding the surface area of a sphere is like finding the total amount of skin on the apple, and the only thing we need to know in order to solve for the surface area of a sphere is its radius.

Help Me Remember This πŸ™πŸΏπŸ™πŸ»πŸ™πŸ½

You can imagine that the sphere is being wrapped around by a cylinder:The surface area of the sphere is equal to the area of the rectangle we use to wrap the sphere:
Let’s put this formula to use by doing a couple example problems where we solve for the surface of a sphere!

EXAMPLE 1

Let's say we know our sphere has radius . What is the surface area?

Step 1. Determine if you’re solving for volume (V) or surface area (SA).

We're looking for the surface area, which is the area of the surface of the sphere.
The formula for finding the surface area of a sphere is:

Step 2. Find the radius of the sphere.

The radius is given to us and is equal to .

Step 3. Calculate the surface area with the radius.

Our answer is .

EXAMPLE 2

Great job! Try one more - say the radius . What is the surface area?

Step 1. Determine if you’re solving for volume (V) or surface area (SA).

We're looking for the surface area, which is the area of the surface of the sphere.
The formula for finding the surface area of a sphere is:

Step 2. Find the radius of the sphere.

The radius is given to us and is equal to .

Step 3. Calculate the surface area with the radius.

Our answer is .
Awesome! If you’d like to practice additional problems finding the surface area of spheres, expand the
Practice
below before closing out this lesson! ⚑
PRACTICE
β€” Surface Area of Spheres

Practice: Surface Area of a Sphere

Question 1 of 3: What is the surface area of a sphere with ?

Step 1. Determine what you are solving for.

Image of Apple
Finding the surface area of a sphere is like finding the total amount of an apple.
Nice! Since we’re solving for surface area, which equation should we use?
That's right! The formula for the surface area of a sphere is
Looks like we’re ready for the next step!

Step 2. Find the radius of the sphere.

What is the sphere's radius?
Nice work! Now plug in:

Step 3. Calculate the surface area with the radius.

Awesome! The surface area of the sphere is Β .

CONCLUSION
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Dang, look at you go! Thanks for checking out this lesson β˜ΊοΈπŸ™. Where to next?
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