Book edition 7th

Author(s) Douglas C. Giancoli

Pages 978 pages

ISBN 978-0321625922

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Short Answer

What, roughly, is the percent uncertainty in the volume of a spherical beach ball of radius $r = 0.84 \pm 0.04 m$ ?

The correct answer of percent uncertainty is 10%.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Writing the given data

Volume is defined as the amount of space that a particular object or body occupies in the space.

The radius of the spherical beach ball, $r = 0.84 \pm 0.04 m$ .

Step 2: Writing the formula of the volume of a sphere

The formula of the volume of a sphere is

$V = \frac{4}{3} π r^{3} \dots (i)$

Step 3: Calculating the volume of the spherical beach ball

From equation (i), the volume is

$V = \frac{4}{3} π {(0.84)}^{3}$ .

Thus, the final value of the multiplication is 0.6%.

Step 4. Writing the formula for a small change in volume

Differentiating equation (i) w.r.t to radius,

$\frac{d V}{d r} = \frac{4}{3} π 3 r^{2} d r$ .

The formula of the small change in the volume of a sphere is

role="math" localid="1643623569468" $d V = 4 π r^{2} d r \dots (i i)$ .

Step 5. Calculating the value of a small change in volume

From equation (ii), the small change in the volume is

$d V = 4 π {(0.84)}^{2} (0.04)$ .

Step 6. Writing the formula of percent uncertainty

The formula of percent uncertainty is

$V' = \frac{d V}{V} \times 100 % \dots (i i i)$ .

Step 7. Calculating the value of percent uncertainty

From equation (iii), the value of percent uncertainty is

$\begin{matrix} V' = \frac{4 π {(0.84)}^{2} (0.04)}{\frac{4}{3} π {(0.84)}^{3}} \times 100 % \\ \approx 10 % \end{matrix}$

Thus, the final value is 10%.

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Physics Principles with Applications

Answers without the blur.

Short Answer

What, roughly, is the percent uncertainty in the volume of a spherical beach ball of radius $r = 0.84 \pm 0.04 m$ ?

Step by Step Solution

Step 1. Writing the given data

Step 2: Writing the formula of the volume of a sphere

Step 3: Calculating the volume of the spherical beach ball

Step 4. Writing the formula for a small change in volume

Step 5. Calculating the value of a small change in volume

Step 6. Writing the formula of percent uncertainty

Step 7. Calculating the value of percent uncertainty

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Physics Principles with Applications

Answers without the blur.

Short Answer

What, roughly, is the percent uncertainty in the volume of a spherical beach ball of radius r=0.84±0.04m?

Step by Step Solution

Step 1. Writing the given data

Step 2: Writing the formula of the volume of a sphere

Step 3: Calculating the volume of the spherical beach ball

Step 4. Writing the formula for a small change in volume

Step 5. Calculating the value of a small change in volume

Step 6. Writing the formula of percent uncertainty

Step 7. Calculating the value of percent uncertainty

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