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As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 $\mathrm{cm}$ and a thickness of 0.050 $\mathrm{cm} .$ Find (a) thevolume of a single cookie and (b) the ratio of the diameter to the thickness, and express both in the proper number of significant figures.

a) 2.8$(\mathrm{cm})^{3}$b) 170

Physics 101 Mechanics

Chapter 1

Models, Measurements, and Vectors

Physics Basics

Cornell University

University of Michigan - Ann Arbor

McMaster University

Lectures

04:16

In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.

09:56

In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

05:23

As you eat your way throug…

06:47

04:14

02:37

A chocolate cookie is a ci…

01:44

00:47

The circumference of a cir…

00:15

01:27

Obtain the difference in v…

03:39

Identify each measurement …

02:10

One sphere has a radius of…

10:04

In the manufacturing of co…

06:21

02:23

Solve. Round answers to th…

This is Chapter one problem. 52 about chocolate chip cookies in the first part. We're looking for the volume of a cookie, and we're told the cookie is a circular disk and we are given the diameter of the cookie. 8.5 centimeters, 8.50 centimeters. Excuse me, because in this problem we are asked to carefully keep track of significant figures so that zero is important because that zero is significant and the thickness is 0.50 centimeters. And I want to call that H because that's basically the height of a cylinder. There's an extremely thin chocolate chip cookie, by the way. All right, so volume of a cylinder is going to be the area of the circle on one end area. Their times the height, age, an area of a circle is pi r squared. So we thought volume equals hi r squared and our our radius is just half the diameter, so I can put in diameter over to you that squared times eight. So we pulled me in looking in 8.5 centimeters for the diameter, 0.50 centimetres for the height. And you end up with 2.8 centimetres huge and, in terms of the number of significant digits, noticed that our input values for the diameter we have three significant digits. But for the thickness, we've only got two. That 0.0 is just telling you, just telling you what I ordered, man into your number. Is that the five and this hero that comes after it? Those are the two significant figures here. So since we've multiplied together a bunch of numbers, the significant the number of significant figures in the output should be the least number of significant figures in any of the inputs. And that would be too two's in different years. We did divide the diameter by too, but that that dividing my chew, that is a an exact number. I could have put 2.0 an infinite amount of precision. So we're not actually counting significant figures there, All right in part B, it wants the ratio of the diameter to the thickness, so we just take the diameter were given and divided by the thickness, and the same rule for significant figures applies essence multiplying and dividing Have the same rules here. So we're dividing something with three significant figures. Buy something with only two. So the answer should be expressed to two significant figures. And since this is the ratio between lengths, those centimeters air going to cancel and you end up with 1.7 times 10 30 we could also write this as 170. But when you put it in scientific notation, it's easier to be really clear about how many figures are significant when you put it. Write it this way. You don't have to write another zero after the seven. That may or may not be significant, just in order to say what order? Gratitude. Your answer is so I put it like this. 1.7% of the two is the ratio between diameter to thickness. Again, this is an extremely thin chocolate chip cookie.

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