Volume of Cone, Cylinder and Sphere - 3D Printing in Mathematics

Описание: We use containers of different shapes and sizes to measure ,transfer as well as store things. Amount of quantity stored depends on the shape as well.

Let us explore how shapes of similar dimensions are related in terms of storage capacity. In technical terms - Volume of the container.

We will consider 3 shapes Sphere, Cylinder and Cone . These are hollow shapes so that we can measure volume. Radius and height of all the containers are equal. 3D printing these containers gives us control over the dimensions.

We will use sand to fill each container. Let us place these on a paper. Sand spilled during the transfer can be collected on this paper and put back in the container.

Let us start with a Cone. We will fill it completely. Let us remove any excess sand with the help of a ruler. Contents of the cone can be emptied into the cylinder.

How many cones do you think can fill the cylinder completely ?

Three sandful of cones are required to fill one cylinder completely.

How about Sphere ? Let us repeat the same process.

It's not very easy to pour sand through this tiny hole. We will use another cone made from plastic sheet for this purpose.

It turns out that we need four coneful of sand to fill this sphere completely.

It's hard to see inside this sphere. We can repeat the same activity with these two hemispheres which are cut from this one sphere.

How many cones of sand is required to fill one hemisphere ?

Two. You guessed it right.

We can say that it takes 3 cones to fill one cylinder while 4 cones are required to fill one sphere. This is true only when the radius of all the shapes is same and height and radius of the cone are equal.

How about actual dimensions ?

We can use a ruler to find out but its better to use a vernier caliper to measure the inside diameter. Digital one is still better.

For the cone and cylinder, the inside diameter is approximately 60 mm. Radius will be 30 mm OR 3 cm.

Height of the Cone is 30 mm or 3 cm.
With all this data, can you refer to your textbook and verify our findings ?

Give it a try.

If you don't have sand, you can use rangoli or similar material for this purpose.

How about using water ? Will it give correct results ? Think about it.

Ratio of volume for these shapes holds good for other dimensions as well.

All files used for 3D printing these objects are available for download so that you can try the same in your ATL tinkering lab.

Thank You.

Link for all the 3D shapes used in this activity

https://www.thingiverse.com/thing:535...




#3dMath
#mensuration
#mathematics