Solve the given problems.What is the area of a paper label...

Name: Problem 42, Chapter 2: Basic Technical Mathematics with Calculus
Uploaded: 2021-06-21T14:28:14-08:00
Duration: 4 min 45 s
Channel: Barsha Rana
Description: Solve the given problems.What is the area of a paper label that is to cover the lateral surface of a cylindrical can 3.00 in. in diameter and 4.25 in. high? The ends of the label will overlap 0.25 in. when the label is placed on the can.

Solve the given problems.What is the area of a paper label that is to cover the lateral surface of a cylindrical can 3.00 in. in diameter and 4.25 in. high? The ends of the label will overlap 0.25 in. when the label is placed on the can.

Key Concepts

Lateral Surface Area

The lateral surface area of a cylinder represents the area of the side surface that connects the circular bases. It is calculated by multiplying the circumference of the circular base by the height of the cylinder, which gives a measure of the rectangular surface that wraps around the cylinder.

Circumference

The circumference is the distance around the edge of a circle. For a circle, it is computed using the formula C = ?d, where d is the diameter. This measurement is critical in determining the effective width of material needed to cover a curved surface, such as the label on a cylindrical can.

Geometric Adjustments for Overlap

In many practical applications, additional material may be required beyond the exact geometric dimensions to allow for overlap or seam allowances. This extra measurement, added to the calculated circumference, ensures that the covering material properly fits or adheres to the curved surface by providing a margin that can be overlapped for secure attachment.

Transcript

00:01 Welcome to numerate in the current problem we are given with a very different kind of a problem.

00:11 What does it say? it says that what is the area of the paper label? so imagine this is a paper, generally paper or anything will be there.

00:20 And there is a correct.

00:25 There is a cylindrical can which is 3 in diameter.

00:31 So d is equal to 3.

00:33 3 centimeters inches to be specific so r will be 1 .5 inches and the point is 4 .25 inches okay 4 .25 now they're telling what area of paper will be needed okay so how much paper will be needed if you want to completely cover it okay so imagine a bottle of a cold drink correct so there will be a bottle of cold drink when you drink and that has a label if you see and if you just open that label it is in general it looks a circular thing but when you open it it will be a long piece of paper like this so we are interested to know that area so for this also for this also this will be 4 .25 correct now how much should be the area so that it can cover this cylindrical can also there will be an overlap there will be an area of overlap that means when this paper gets folded like this so it should overlap only and then they will put a gum over here right so when something overlaps like that okay that that width is mentioned to be 0 .25 inches, 0 .25 inches, okay, that area.

02:06 So now we are interested to know that how much paper we will require.

02:12 Now, let us see, h is mentioned as 4 .25 inches, correct, as we already pointed it out.

02:21 Now, think of what will be the, this or like whatever, this, this, this thing, how can we obtain it.

02:30 If you think 2 pi r is the, 2 pi r is the circumference, then those many 2 pi are if we stack on each other, we will find this area, right? so the height, so it will be 2 ,5 rh plus.

02:48 Now we also want to know how much will be the overlap area.

02:52 Overlap area will have this 4 .25 height and 0 .25...

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