Question

If the radius of a circle is r=3.0 +- 00 calculate the circumference of it's circle and it's uncertainty

Answer 1

Explanation:

Volume of the sphere: V=

3

4

πr

3

Differentiating with respect to r

dr

dV

=

3

4

π.3r

2

⇒

dr

dV

=

3

4

πr

3

.

r

3

⇒

V

dV

=

r

3dr

Or

⇒

V

ΔV

=

r

3Δr

Step 2: Percentage error in the volume

Given: r=5.3±0.1 cm

So, Δr=0.1cm and r=5.3cm

Percentage error in volume=

V

ΔV

×100%=

5.3 cm

3×0.1 cm

×100%=5.66%