yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Area of a circle | Perimeter, area, and volume | Geometry | Khan Academy


3m read
·Nov 11, 2024

  • [Teacher] A candy machine creates small chocolate wafers in the shape of circular discs. The diameter, the diameter of each wafer is 16 millimeters. What is the area of each candy?

So, the candy, they say it's the shape of circular discs. And they tell us that the diameter of each wafer is 16 millimeters. So if I draw a line across the circle that goes through the center, the length of that line all the way across the circle through the center is 16 millimeters.

So let me write that, so diameter, the diameter here is 16 millimeters and they want us to figure out the area, the area of the surface of this candy. Or essentially the area of this circle. And so when we think about area, we know that the area of a circle, the area of a circle is equal to pi times the radius of the circle squared.

Times the radius of the circle squared, and you say, well they gave us the diameter, what is the radius? Well, you might remember the radius is half of diameter, so distance from the center of the circle to the outside, to the boundary of the circle.

So it would be this distance right over here, which is exactly half of the diameter. So, it would be eight millimeters. So, where we see the radius, we could put eight millimeters.

So the area is going to be equal to pi times eight millimeters squared, which would be 64, 64 square, 64 square millimeters. And typically, this is written with pi after the 64, so you might often see it as this is equal to 64 pi, 64 pi millimeters squared, millimeters squared, millimeters squared.

Now, this is the answer, 64 pi millimeters squared, but sometimes it's not so satisfying to just leave this pi, you might say, "Well, I wanna get an estimate of what number this is close to, I wanna decimal representation of this."

And so we can start to use approximate values of pi. So, the most rough approximate value that tends to be used is saying that pi, a very rough approximation is equal to 3.14. So in that case, we could say that this is going to be equal to 64, 64 times 3.14 millimeters, millimeters squared and we can get our calculator to figure out what this will be in decimal form.

So we have 64 times 3.14 gives us 200.96. So we could say that the area is approximately equal to, approximately equal to 200.96 square millimeters.

Now, if we wanna get a more accurate representation of this, pi actually just keeps going on and on and on forever, we could use the calculator's internal representation of pi. In which case we'll say 64 times and then we have to look for the pi in the calculator, it's up here in this yellow so I'll do this little second function, get the pi there, every calculator will be a little different.

But 64 times pi, now we're going to use the calculator's internal approximation of pi, which is going to be more precise than what I had in the last one and you get 201, so let me put it over here so I can write it down, so a more precise is 201, and I'll round, I'll round to the nearest, I'll round to the nearest hundredth so you get 201.06, so 201, so more precise is 201.06 square millimeters.

So this is closer to the actual answer 'cause a calculator's representation is more precise than this very rough approximation of what pi is.

More Articles

View All
The Secret Life of Plants | Podcast | Overheard at National Geographic
I’m looking at what you might call a classic National Geographic image. It’s a scene of one of the rainiest places on earth in its monsoon season. It’s somewhere deep in a rainforest. There’s a lush tapestry of thin brown tree trunks and rich green leaves…
How Your Toothbrush Became a Part of the Plastic Crisis | National Geographic
(Tapping) [Narrator] Hopefully you know this already but … that’s a toothbrush. So are these. And the one thing they have in common: they’re all plastic. But here’s something you might not know. This routine has been around for a millennia. And back then…
You Can't Touch Anything
Hey, Vsauce. Michael here. And today we’re going to get close, like really close. In fact, I want to answer the question: what’s the closest we can get to other objects and other people? Now, it might sound like kind of a simple, easy question, but when …
How to Measure Happiness Around the World | National Geographic
Can you measure happiness? It’s not an easy task, but every year the Gallup World Poll tries to estimate how happy people are in a hundred and forty countries around the world. Where do they even start? Frequency of smiley face emojis? Number of hugs give…
Wabi-Sabi | A Japanese Philosophy of Perfect Imperfection
The pursuit of perfection has become the norm in today’s world, where chronic dissatisfaction, burnout, depression, and anxiety reign supreme. We’ve subjected ourselves to unrealistic standards and rigorously chase an ideal that’s impossible to reach. Adv…
The End of Robinhood..
What is up, finance alert nation? I am your host, Graham Stefan, and let’s get right into the news. Just kidding! I’m starting to feel a little bit like the drama alerts of finance lately, because we haven’t seen this much money-related drama since last w…