## Introduction: Measuring Cup - Measuring Volumes

*The following information is a single lesson in a larger Tinkercad project. Check out this and more projects on *Tinkercad*.*

**Return to Previous Lesson: **Ruler - Measuring Lengths

**Lesson Overview:**

Now we're going to make a cup!

## Step 1: Introduction

In this lesson, we're going to learn how to make a tool for measuring volume!

Volume is how much space an object takes up. An object that has length and width and height is taking up volume…like the objects in Tinkercad!

However, volume measures are often for materials that don't have a uniform shape like liquids, powders, grains, and pebbles.

__Instructions__

- Continue to the next step.

## Step 2: Creating the Volume for Your Measuring Cup

We are going to start using a cylindrical volume of 20ml as an example. In Steps 7 and 8, you have the tools to create the volume of your choice.

Work with your class to create a set of volumes!

__Instructions__

- Drag out a cylinder to the Workplane.
- Size it as per your desired calculations, and make it a hole. My 20ml volume will be a cylinder that is 30mm in diameter and 30mm tall along the Z axis.
- Continue to the next step.

## Step 3: Creating the Vessel

We're going to print the cup facing down to make 3D printing the handle easier.

In this step, we are creating the cup around our volume.

__Instructions__

- Duplicate your shape and make it solid again.
- Grow the object by 6mm along the X and Y axes and 3mm along the Z axis.
- Center the two cylinders along their X and Y axes but to their lower Z axis limits.
- Continue to the next step.

## Step 4: Create the Handle

Now we'll create a simple handle that has enough room for some text describing the volume.

__Instructions__

- Drag out a Round Roof and align it so that it extends out from the center off the cylinders.
- Grow the round roof until it extends roughly 4cm from the side of the cylinder. Because every volume is different, the length of this object will be different for everyone.
- Shrink the round rood to 5mm tall along the Z axis.
- Drag out a Hemisphere, shrink it to 5mm tall along the Z axis, and align it to the end of the round roof so that it creates a smooth tangent.
- Continue to the next step.

## Step 5: Create the Label

A measuring instrument is no good if it's not labeled! So we're going to do that, now.

Tinkercad has number and letter shapes, but it only has upper case letters. Why is this important? Because ML doesn't mean Milliliters, it means MEGALITERS! We don't have the time to make a measuring cup that big!

So to make a label with lowercase letters, we're going to use the Text Shape Generator in the Shapes menu.

__Instructions__

- Drag out the Text Shape Generator under the Tinkercad collection.
- Choose the font "Arimo" and type out the volume you have chosen.
- Mirror the text so it can be read from the bottom.
- Continue to the next step.

## Step 6: Positioning the Label

Now we just need to put the label on our handle!

__Instructions__

- Proportionally scale the text until it is 10mm tall along the Y axis and then shrink the text along the Z axis until it is 1mm tall.
- Align the text to the handle's center along the Y axis and nudge the text in to position along the X axis.
- Select all the objects and group them.
- Continue to the next step.

## Step 7: Calculating the Volume of a Cube

The metric system was designed around a volume of water in a 1cm cube. This volume was named the Milliliter (ml).

The volume of a cube is the area (length times width) of a sides multiplied by its height, or x^3.

However, in this lesson, we want to find the dimensions of a cube from a known volume. Instead of cubing a side, we can take a cube root of a volume. For example, a liter is a cube with 10cm sides :

10=∛(1000)

Both Apple OSX and Microsoft Windows come with calculators with the cube root function.

__Instructions__

- Continue to the next step.

## Step 8: Calculating the Volume of a Cylinder

Like with a cube, we calculate the volume of a cylinder by multiplying the area of a side by its height. Finding the volume of a cylinder is challenging because its sides are circles. Fortunately, thousands of years ago, we found a number that helps us, and that number is 'pi' or 'π'.

Pi is the ratio between the diameter of a circle and its circumference. The formula for the area of a circle is:

Area=pi*d^2/4

If we make the height and the diameter the same, this is easy to solve, we simply raise the square to a cube:

Volume=pi*d^3/4

But what if we know the volume and want to figure out the diameter and height? We solve for diameter:

d=∛((4*Volume)/pi)

So if you want a cylindrical volume of 1L (or 1000cm3), your diameter and height should be:

~10.9cm=∛((4*1000)/pi)

__Instructions__

- Continue to the next step.

## Step 9: Printing

Congratulations, you've completed Lesson 2 of Making Your Own Measurement Tools! Well done! Now let's try printing your measuring cup.

No matter how you orient this object, there will be overhangs. Therefore, during the building process, we built it in the orientation that has the least overhangs.

If you make a larger volume, it may make sense to flip the object over if you think the handle would require less support material than supporting the bottom of the cup.

__Instructions__

- From the Design menu, click "Download for 3D Printing."
- Click the button labeled "STL."
- When your browser has completed downloading, load the file into your 3D printer software.
- This object has some overhangs, so make sure to enable "Support Structure" in your 3D printer software.
- Print!

In the next lesson you will learn to make a protractor!

**Next Lesson:**Protractor - Measuring Angles

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