BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.6, Problem 78E
To determine

To find: The radius of large sphere.

Expert Solution

Answer to Problem 78E

The radius of large sphere is 4.63 mm.

Explanation of Solution

Given:

The radius of three small solid spheres is 2 mm, 3 mm and 4 mm.

Formula used: Volume of sphere

Volume=43π(radius)3

Calculation:

Let the radius of sphere be x.

Tabulate the given information into the language of algebra.

In words In algebra
Radius of large sphere x
Volume of large sphere 43πx3

Model the equation for the above information.

Volumeoflargesphere=Sumofvolumeofallspehers43πx3=43π(2)3+43π(3)3+43π(4)3

Simplify the above equation for x,

43πx3=43π[(2)3+(3)3+(4)3]x3=8+27+64x3=99x=4.63

Thus, the radius of large sphere is 4.63 mm.

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