Video: Finding the Circumference of a Circle given Its Radius in a Real-Life Context

Three forces act on a particle, which moves with constant velocity 𝑣 = (3𝐢 − 2𝐣) m/s. Two of the forces are 𝐅₁ = (3𝐢 + 5𝐣 − 6𝐤) N and 𝐅₂ = (4𝐢 − 7𝐣 + 2𝐤) N. Find the third force, 𝐅₃.


Video Transcript

A cylinder-shaped jar of jam has a circular base of radius seven. Use twenty two over seven as an approximation of 𝜋 to calculate the perimeter of the base.

Okay, let’s draw a quick sketch of our jar of jam. It’s a cylinder shape, so there it is. And we’re told that it has a circular base of radius seven units. We’re not told what those units are so we won’t be able to write those down, but seven units. So the radius is the distance from the centre of a circle to its circumference.

Now we’re trying to work out the length of the perimeter of the base. We’re told the base is a circle so we want to know the perimeter of a circle radius seven. Now we’ve got two possible formulae that we could work with. We could do 𝜋 times the diameter of the circle or we could do two times 𝜋 times the radius of the circle. Now we’ve been given the radius in this case, so we’re gonna use the second of those formulae.

So that’s two times, and then we were told to use twenty-two over seven as an approximation of 𝜋, so we’re gonna write two times twenty-two over seven. And we were told that the radius was seven.

So our calculation becomes two times twenty-two over seven times seven. Now I’m gonna turn this into a proper fraction calculation. But instead of writing two, I’m gonna write two over one. And instead of writing seven, I’m gonna write seven over one. And now when we’re multiplying fractions together, I can just multiply all the tops together and then all the bottoms together, all the numerators together and then all the denominators together. But before I do that, I can see that I’ve got a seven as one of the numerators but I’ve also got a seven as one of the denominators, so I can do some cancelling. If I do seven divided by seven, I get one. If I do seven divided by seven, I also get one. So I’ve got two over one times twenty-two over one times one over one.

Well two times twenty-two times one is forty-four, and one times one times one is one. Well forty-four over one is just the same as forty-four. And we weren’t told specifically what the units were, so I’m just gonna write forty-four units. So there we have our answer: forty-four units.

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