Surface area and volume of spheres

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

0/0
?
Intros
0/2
?
Examples
Lessons
  1. Find the surface area and the volume of the following shapes:


    1. Surface area and volume of spheres

    2. Surface area and volume of half spheres
Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
  • Easily See Your Progress

    We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
  • Make Use of Our Learning Aids

    Last Viewed
    Practice Accuracy
    Suggested Tasks

    Get quick access to the topic you're currently learning.

    See how well your practice sessions are going over time.

    Stay on track with our daily recommendations.

  • Earn Achievements as You Learn

    Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
  • Create and Customize Your Avatar

    Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
Topic Notes
?
A basketball is a sphere. Soap bubbles are usually spheres. A vitamin capture is a combination of cylinder and sphere. In this lesson, we will learn how to calculate the surface area and volume of spheres and composite solids.

What is hemisphere?

Hemispheres are half of spheres. If you took a sphere and cut it exactly in half, you'd have two hemispheres! So for example, a sphere is a ball shape. Cutting it in half will give us two hemispheres of a ball. We'll be working with both spheres and hemispheres in this lesson in order to find surface area and volume.

 

How to find the surface area of a sphere

The surface area is the sum of all the surface areas of a shape's sides. In the case of a sphere, the formula for this is:

Surface area = 4π\pir^2

 

How to find the volume of a sphere

The volume of a sphere tells us how much space there is inside a sphere. How to find volume of a sphere? There's a simple formula for that and it is:

Volume = 4/3 π\pir^3

 

How to find the surface area of a hemisphere

Let's try out an example that uses the surface area formula for spheres. We're actually not going to deal with a sphere, but a hemisphere.

 

Question:

Find the following object's surface area:

Surface area and volume of spheres
Surface area and volume of spheres

 

Solution

 

A hemisphere, as we learned previously, is half of a sphere. Keep this in mind as we work through this problem.

 

The formula for the surface area of a sphere is:  4π\pir^2. To find out the hemisphere's surface area, we can divide this formula by 2 which gives us:  4π\pir^2/2. But don't forget that the bottom of the hemisphere now also becomes a surface and will have its own surface area. It's shaped like a circle, and therefore, its surface area is equalled to π\pir^2 as we have learned in past lessons. Therefore the formula for our hemisphere is:

4π\pir^2/2 + π\pir^2

 

We'll first need to find the radius. We've learnt from previous lessons that the diameter = 2r, so we can make use of this to help us find the radius.

 

D = 2r

20 = 2r

r = 10 ft

 

Now we can plug the radius into the formula to solve for the hemisphere's surface area.

Surface area of a hemisphere = 4π\pir^2/2 + π\pir^2

SA = [4π\pi(10^2)]2 + π\pi (10)^2

SA = 942.48 ft^2

 

The area of hemisphere equals to 942.48ft^2. Remember that finding surface area will give you answers in squares. Also, do not forget the unit!



How to find the volume of a hemisphere

Let's move on to finding the volume of a hemisphere.  

 

Question:

Find the following object's volume:

Surface area and volume of spheres
Surface area and volume of spheres

Solution:

For the volume, all you'll need to do is to take the formula for a sphere's volume and then divide it by 2. The sphere's formula is Volume = 4/3 π\pir^3, and for a hemisphere, we'll use Volume = (4/3 π\pir^3)/2.

 

In terms of calculation we've got:

Volume = (4/3 π\pir^3)/2

V = [4/3 π\pi(10^3)]/2

V = 2094.4ft^3

 

We get that the volume of hemisphere equals 2094.4ft^3. In this case, since we're finding the volume, the answer will be given in cubic form. Once again, do not forget the unit, which is in feet for this problem.

 

To see the relationship of the volume and the radius, and how they affect one another, check out this helpful click-and-drag diagram!


equations of area,surface area,and volume of spheres