Question

Help me please! 8-1

Use a formula to find the amount of wrapping paper you need to wrap a gift in the cylindrical box shown. You need to cover the​ top, bottom, and all the way around the box. Use 3.14 for .
​(The figure is not to​ scale.)
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Part 1
You need about

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in. of wrapping paper.
​(Round to the nearest tenth as​ needed.)

Answer 1

Answer: 414.5

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Step-by-step explanation:

The surface area of a cylinder is

SA = 2*pi*r^2 + 2pi*r*h

The 2*pi*r^2 portion handles the 2 identical flat circular faces on top and bottom (each being area of pi*r^2). The 2*pi*r*h portion handles the curved side.

We'll plug in the radius of r = 6 and height of h = 5

SA = 2*pi*r^2 + 2pi*r*h

SA = 2*pi*6^2 + 2pi*6*5

SA = 2*pi*36 + 2*pi*30

SA = 2*36pi + 2*30pi

SA = 72pi + 60pi

SA = 132pi

That's the exact surface area in terms of pi.

Your teacher wants you to replace pi with the approximation 3.14

SA = 132pi

SA = 132*3.14

SA = 414.48

Then as a final step, we round to the nearest tenth (aka 1 decimal place) to get 414.5 square inches

Answer 2

The total surface area of the cylinder is: A = 414.5 in²

What is the surface area of the cylinder?

The formula for the total surface area of the cylinder is:

A = 2πr² + 2πrh

where:

r is radius

h is height

Thus:

A = (2 * 3.14 * 6²) + (2 * 3.14 * 6 * 5)

A = 414.5 in²