   Chapter 10.6, Problem 40E 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 sphers x - 1 2 + y + 2 2 + z - 4 2 = 36 and x 2 + y 2 + z 2 = 64 , find the ratio of theira) surface areas.b) volumes.

To determine

(a)

To find:

The ratio of surface area of two spheres x-12+y+22+z-42=36 and

x2+y2+z2=64.

Explanation

Let the equation of sphere 1 is x-12+y+22+z-42=36

Let the equation of sphere 2 is x2+y2+z2=64

The equation of the sphere with center h, k, l and radius length r is given by

x-h2+y-k2+z-l2=r2

Writing the given equation in the form of the general equation.

x-12+y--12+z-42=62

From this, r=6

Finding the surface area of sphere 1.

Surface area of sphere =4π62

Multiplying,

Surface area of sphere =4π36

Surface area of sphere =144π square units.

The equation of the sphere with center 0, 0, 0 and radius length r is given by

x2+y2+z2=r2

Writing the given equation in the form of the general equation

To determine

(b)

To find:

The ratio of volume of two spheres x-12+y+22+z-42=36 and

x2+y2+z2=64.

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