   Chapter 9.3, Problem 39E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

For the two similar cylinders in Exercise 38 , what is the ratio of the lateral area of the larger cylinder to that of the smaller cylinder?If the length of the radius and the height of a right circular cylinder are both doubled to form a larger cylinder, what is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder?(Note: The two cylinders are said to be “similar.”)

To determine

To find:

The ratio of the lateral area of the larger cylinder to the lateral area of the smaller cylinder.

Explanation

Given:

The radius and height of a right circular cylinder are both doubled to form a larger cylinder.

Formula used:

The lateral area of the right circular cylinder is L=πrl.

Calculation:

Let r be the radius of the base and h be the height of the right circular cylinder.

Let L1 be the lateral area of the smaller cyliner.

L1=2πrh.

The radius and height of a right circular cylinder are both doubled to form a larger cylinder.

That is, radius is 2r and the altitude is 2h.

Let L2 be the lateral area of the larger cylinder.

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