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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±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±0.04m.

02

Writing the formula of the volume of a sphere

The formula of the volume of a sphere is

V=43πr3…(i)

03

Calculating the volume of the spherical beach ball

From equation (i), the volume is

V=43π0.843.

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=43π3r2dr.

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

role="math" localid="1643623569468" dV=4πr2dr…(ii).

05

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

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

dV=4π0.8420.04.

06

Step 6. Writing the formula of percent uncertainty

The formula of percent uncertainty is

V'=dVV×100%…(iii).

07

Step 7. Calculating the value of percent uncertainty

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

V'=4π0.8420.0443π0.843×100%≈10%

Thus, the final value is 10%.

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