   Chapter 9.CR, Problem 20CR 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

If the radius length of one sphere is three times as long as the radius length of another sphere, how do the surface areas of the spheres compare? How do the volume compare?

To determine

To compare:

The surface area of the spheres and the volume of the spheres.

Explanation

Formula used:

Surface area of sphere:

S=4πr2

Volume of sphere:

V=43πr3

Given:

If the radius length of one sphere is three times as long as the radius length of another sphere.

Calculation:

Let us consider the small sphere and large sphere as shown in the figure.

The above figure shows that the radius length of one sphere is three times as long as the radius length of another sphere.

The surface area of small sphere is S=4πr2.

The surface area of large sphere is S=4π(3r)2.

So, we compare the surface area of spheres,

Surface area of smallerSurface area of larger=4πr24π(3r)2=r232r2Surface area of smallerSurface area of larger=19

Then, we compare the volume of spheres,

The volume of small sphere is V=43πr3

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