Volume of Cones and Spheres
Aligned To Common Core Standard:
Geometric Measurement - HSG-GMD.A.3
How to find the Volume of Cones and Spheres - We all have enjoyed ice cream cones and kicking the ball around in the park. But do you know we have a different name for favorite ice-cream cones and footballs? Your favorite ice-cream cones are termed as cones, and your curved ball is known as a sphere. Cone Shapes - A cone is a 3D shape that has one edge and two faces. Generally speaking, they have a point at one end and a circle at the other end. Unlike most shapes, they are not a polyhedron, i.e., it doesn't have flat faces. Its circular and pointy ends are completed with a curved surface. The flat part is known as the base, and the pointy end is termed as the apex Volume of a Cone - The formula for cone is similar to that of a cylinder. In fact, it is exactly one-third of cylinder's volume formula Volume of a cylinder is: V = Π x r2 x h And to find the volume of a cone, we use the formula:V = 1/3 x Π x r2 x h Where 'r' is the radius of the circle at the wide end and 'h' is the height. Spheres - A perfectly symmetrical 3D shape with one continuous surface and zero edges or vertices. Spheres, unlike cones, are not a polyhedron. Every point on the sphere's surface is equidistant from its center. We calculate the volume of the sphere by using the formula: V = 4/3 x Π x r3 | Where 'r' is the radius of the sphere. These worksheets and lessons will show you how to calculate these measures and help you make sense of it.
Printable Worksheets And Lessons
- Cone Volume Step-by-step Lesson - Figure out the volume of an old fashion ice cream cone.
- Guided Lesson - Cones and spheres all around. What's their volume?
- Guided Lesson Explanation - These problems and the unit, for that matter, are mostly plug into the equation and go.
- Practice Worksheet - Work yourself into surface area.
- Matching Worksheet - I left the units off because it just won't fit without looking chaotic.
A page donated to each skill and then a cumulative page for you.
- Homework 1 - The formula of volume of cone = 1/3 Π r2h. You will get practice solve a bunch of problems along the way.
- Homework 2 - The formula of surface area = 4 Π r2. We calculate these measures on the surface of a sphere.
- Homework 3 - Put this together to find the radius in each case. We apply this to both geometric shapes and learn all their measures.
Cones, cones, and more cones!
- Practice 1 - What is the volume of this cone? Use the techniques that we have discussed here.
- Practice 2 - What is the surface area of this sphere? Make sure that you round your answer to the nearest hundredth.
- Practice 3 - More problems that will challenge you. This provides you with more practice.
Math Skill Quizzes
The difficult is somewhat even across all of these.
- Quiz 1 - Pay attention to the height value. This quiz covers all the skills we are working on.
- Quiz 2 - The radius and height of the cones are provided. Work off of them to fins the measures we are looking for.
- Quiz 3 - You will be asked to round your answer to the nearest hundredth. Remember that this is two places to the right of the decimal.
Let's Take a Look at These Geometric Shapes
An ice cream cone basically sums up these two geometric shapes in one. Take a look at the image below to see what we are saying.
If you think about it where else do you see these shapes, how many can you name? Here are ten common examples of cones that you will come across in your daily routine: party hats, street cones, volcanoes, most trees, a megaphone, teepees, Bugels snacks, most costume noses, a tip of a pencil, dog head cones to protect them from licking themselves. How about spheres, that is a little easier. Here you go: an orange, a class globe, the sun, lollipops, basketballs, baseballs, bowling balls, planets, moons, marbles, and an eye ball.