Scents 4 Cents, a discount perfume company, is about to...

Scents 4 Cents, a discount perfume company, is about to release their latest perfume, but they are unsure which bottle to use. They are considering the three bottles pictured here. 1) What do they need to know about the bottles to make their decision? 2) What do you need to know to find the volume of each figure? 3) Predict: without doing the math, predict which containers do you think hold the most and the least perfume? Order from Least to Greatest Volume 4) How did you know what order to put them in? What reasoning did you use? 5) Why is knowing the volume of each container important to the company?

Transcript

00:01 Okay, so we have these different perfume bottles that we're looking at different shapes.

00:05 We have a sphere, a cylinder cone.

00:09 And question, okay, what do we need to know, or does this company need to know before they start selling whichever one they want? well, the main thing is we need to know what the volume is because that's going to dictate the price, right? so if you're selling more of something, you're going to charge more for it.

00:27 So it's going to be a decision of, okay, based on that, which one do we want to sell? so we can find the volume of each of these.

00:34 Then it asks, okay, so what do we need to know to find the volume? well, it depends on which figure we're looking at.

00:41 So i'm going to write these out here.

00:49 So for a sphere, the volume is four -thirds pi times the radius cube.

00:55 So the radius is from the center to any point on there.

00:58 That's the radius.

00:59 So for a sphere, we need to know the radius.

01:00 That's all we need.

01:01 And everything else we're good with.

01:03 For a cylinder, it's pi r squared times the height.

01:09 So we have the radius down here of the base, and then the height is how high it reaches.

01:15 So we need two things for a cylinder.

01:16 We only need one for a sphere.

01:21 A cone has almost the same volume as a cylinder, except there's a one -third involved.

01:28 So we still have a radius for the base.

01:29 We still have the height.

01:30 Everything else is the same.

01:37 So that's the things we need.

01:39 Now we're asked to make a prediction.

01:42 Based on the pictures, which go volume from largest to smallest.

01:48 So we're going to assume they all have the same height because they look like they do in the picture.

01:51 We're going to assume that because we don't really know for sure.

01:54 So we could calculate this mathematically.

01:56 There is a way we can do that.

01:58 I'll kind of talk about that briefly...

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