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圓的面積 (英): 圓的面積
- A candy machine creates small chocolate wafers in the shape of circular discs.
- The diameter of each wafer is 16 millimeters.
- What is the area of each candy?
- Of each wafer, I'm guessing.
- So that's a wafer.
- The diameter is 16, so this is the center.
- The diameter is 16 millimeters,
- and they want us to figure out the area.
- So that's, so that's equal to the diameter.
- So the area, and so the, the formula that, one of the famous formulas of geometry,
- for the area of a circle, is pi r squared, where pi is 3.14159 on and on and on...
- the ratio of the circumference of the diameter of the circle.
- r is the radius of the circle.
- So they told us the diameter of the circle,
- and the radius is just half of that, because the radius is half of a diameter.
- So the radius for this circle, for each of these wafers, is going to be 8 millimeters.
- So the radius, that part right there, is going to be 8 millimeters.
- So, the area of our circle is going to be equal to pi times 8 millimeters squared,
- and I'll keep the units there just so that we get the right units for area at the end.
- So area is going to be equal to pi times 64 meters squared,
- or I guess you can call them square meters.
- Or just to write this the way it's typically written,
- area is equal to 64 pi meters squared.
- Now it's important to realize pi is not a variable;
- it literally is representing just a very famous number in mathematics.
- Pi is equal to 3.14159, keeps going on and on without repeating.
- So we literally could take 3.14159 and put it in the place of pi right over here.
- And I'll use a--
- And sometimes people will approximate it with 3.14,
- but I'll just go use a calculator to get the exact value.
- So we could say 64...
- You could just say 64.
- If you want a very rough one, you could say 64 times 3.14,
- which would give you 200.96 millimeters squared.
- But if you wanted a more exact answer, you could literally go off and multiply 64 times pi.
- And I'm sure this calculator has pi stored in it up to some pretty, pretty accurate precision.
- So 64--
- Some pretty precise precision I should say.
- So 64 times pi exactly is 201.06.
- So I'm gonna go with this 'cause this is the more precise answer, 201 point,
- and, and, and to the more accurate answer 201.06.
- So this is 201.06 square, square millimeters.