   Chapter 9.3, Problem 10E 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

Suppose that the volume of an aluminum can is to be 9 π  in 3 . Find the dimensions of the can if the diameter length of the base is three-fourths the length of the altitude.

To determine

To calculate:

The dimensions of the can.

Explanation

Given:

The volume of an aluminum can is 9π in3 whose diameter of the base is three-fourth the length of the altitude.

Formula used:

The volume of the right circular cylinder is V=πr2h.

Calculation:

Let r be the radius, d be the diameter of the base and h be the altitude of the can.

We know, d=2r.

The diameter of the base is three-fourth the length of the altitude.

That is, d=34h

2r=34hr=38h

We have, V=9π cm3,r=38h

Substitute the known values in the formula,

V=πr2h9π=π(38h)2h9π

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