Finding the Volume of Pie Using Pi (π)




About: Interstellar traveller and writer of many things. I make stuff.

Today I will show you how to measure the volume of an object using our helpful mathematical term and irrational number Pi (3.14159265359) π. First of all, thanks to Instructables user MichaelM2015 for making our apple/blueberry pie, and what better object could you use to find the volume with Pi?

Now I’ll give you a little bit of a summarized review on our wonderful Pi before we start measuring the pie itself. Pi is the ratio of a circle’s circumference to its diameter: 3.14. It is the same measurement for circles of any size.

Diameter - a line going through the circle from edge to edge, dividing circle in half.

Circumference - the distance around the circle.

Radius - distance from center to the edge of the circle (exactly half of the diameter)

Pi - 3.14 (of course)

A circle is always a little bit larger than three times its size around. Archimedes, using many-sided polygons, discovered that pi was about 22/7. Recently, Pi has been calculated to over a TRILLION digits past the decimal (click this link to view only 1 million digits of Pi, if you dare). Pi is infinite and patternless and it’s a lot of fun to play with (and memorize, if ye can!), making it humankind’s best beloved irrational numeral. Thank you, Archimedes.

For our math, we are going to be using the number 3.14159, the radius, and the height of the pie. This will be as easy as store-bought pie! Which is pretty simple, if you reread that. Let’s get out our ruler and measure the height and radius of Michael’s pie (and see if I can restrain from nibbling it in the process).


A pie (any size)

A calculator


Pencil and paper (optional)

Step 1: Finding the Radius of the Pie

Let’s find the area of the circle: A = πr2 (Area equals Pi x radius x 2). We're going to measure in inches. Taking our ruler, we measure the diameter of the pie. Ours turned out to be 9.75 in. Using the calculator, we divide the diameter in half and we got 4.875. The radius of our pie therefore is 4.875 in.

Fun fact: Pi day last year was a big deal. The first several digits of pi is 3.1415, and last year’s Pi day date was March 14, 2015 = 3/14/15 = 3.14.15. If that isn’t awesome, I don’t know what is.

Step 2: Square 4.875 in and Multiply It by Pi (3.14159)

Now take your radius and square it. My 4.875 in squared equaled 23.765625 in. Multiply that new number by the infamous one 3.14159. I got 74.661849 in, which is the total area of the base of the pie (because, as you'll remember, the volume of the pie is the base x height; see next step).

Fun fact: Congress passed Pi day in March 2009, designating March 15 (3.14) as the national Pi Day. Thank you, Congress.

Step 3: Multiply 74.661849 X 2 to Get the Whole Volume of the Pie

Now we measure the height of the pie, with the ruler upright against the side (see the picture). I wasn't totally accurate, as you can see the pie dish curves up and out, but we did our best. The total height then, was approximately 2 inches. Now multiply your height by your radius squared x pi. My radius squared times pi: 74.661849. Multiplied that by 2 and that = 149.32369 in3, which is the final answer. And that, my friends, is finding the volume of pie using pi!

I hope you enjoyed the instructable. Now dig in. √-1 2^3 ∑ π and it was delicious!

Pi Day Challenge 2016

Runner Up in the
Pi Day Challenge 2016

Full Spectrum Laser Contest 2016

Participated in the
Full Spectrum Laser Contest 2016



    • 1 Hour Challenge

      1 Hour Challenge
    • Classroom Science Contest

      Classroom Science Contest
    • Pets Challenge

      Pets Challenge

    6 Discussions


    Question 1 year ago on Step 1

    what is 15 multiplied by 3.14 in pi how do you do it i don understand

    1 answer

    Answer 1 year ago

    Not sure what you're asking here. Does it help you if I say that pi is just the name given to that number? The same way that "a dozen" is just a name for twelve


    3 years ago

    My goodness, Susannah, this is amazing! :)

    1 reply