# Thebasic definition of derivative of under root x.

### Precalculus: Mathematics for Calcu...

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

### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 1.5, Problem 122E

(a)

To determine

## To find: Thebasic definition of derivative of under root x.

Expert Solution

Thesphere, cylinder and cone will have equal volume

Vcyl=Vcon=Vs or 43πr3=πr2h1=13πr2h2 .

### Explanation of Solution

Given:

All sphere, cylinder and cone have same radius and same volume.

Concept used:

The volume of the sphere: Vs=43πr3 .

The volume of the cylinder: Vcyl=πr2h1 .

The volume of the cone: Vcon=13πr2h2 .

Calculation:

The volume of the sphere: Vs=43πr3 .

The volume of the cylinder: Vcyl=πr2h1 .

The volume of the cone: Vcon=13πr2h2 .

The sphere, cylinder and cone will have equal volume when its moulded to each other the shape of the structure changes volume remain same due to having geometrical shapes different each of the solid geometry have different formula but equal volume.

Hence, the sphere, cylinder and cone will have equal volume

Vcyl=Vcon=Vs or 43πr3=πr2h1=13πr2h2 .

(b)

To determine

### To find:The equation of the cylinder’s height and cone height.

Expert Solution

The height of the cylinder h1=43r and height of the cone h2=4r .

### Explanation of Solution

Given: 43πr3=πr2h1 and 43πr3=13πr2h2 .

Concept used:

The volume of the sphere: Vs=43πr3 .

The volume of the cylinder: Vcyl=πr2h1 .

The volume of the cone: Vcon=13πr2h2 .

Calculation:

Vs=Vcyl43πr3=πr2h1 .

Dividing by πr2 :

h1=43r .

Vs=Vcon43πr3=13πr2h2 .

Dividing by 13πr2 :

h2=4r .

Hence the height of the cylinder h1=43r and height of the cone h2=4r .

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