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Chapter 1: Q10. (page 18)

What, roughly, is the percent uncertainty in the volume of a spherical beach ball of radiusr=0.84卤0.04m?

Short Answer

Expert verified

The correct answer of percent uncertainty is 10%.

Step by step solution

01

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卤0.04m.

02

Writing the formula of the volume of a sphere

The formula of the volume of a sphere is

V=43蟺r3鈥�(i)

03

Calculating the volume of the spherical beach ball

From equation (i), the volume is

V=43蟺0.843.

Thus, the final value of the multiplication is0.6%.

04

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

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

dVdr=43蟺3r2dr.

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

role="math" localid="1643623569468" dV=4蟺r2dr鈥�(ii).

05

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

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

dV=4蟺0.8420.04.

06

Step 6. Writing the formula of percent uncertainty

The formula of percent uncertainty is

V'=dVV脳100%鈥�(iii).

07

Step 7. Calculating the value of percent uncertainty

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

V'=4蟺0.8420.0443蟺0.843脳100%鈮�10%

Thus, the final value is 10%.

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Most popular questions from this chapter

A storm dumps 1.0 cm of rain on a city that is 6 km wide and 8 km long in a 2 h period. How many metric tons (1 metric ton =103kg) of water fell on the city? (1cm3of water has a mass of1g=10-3kg.) How many gallons of water was this?

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What is the percent uncertainty in the measurement5.48卤0.25m?

For an answer to be complete, the units need to be specified. Why?

Write the following as full (decimal) numbers without prefixes on the units: (a) 286.6 mm, (b) 85 渭V(c) 760 mg, (d) 62.1 ps, (e) 22.5 nm, (f) 2.50 gigavolts.
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