Units and Measurements

Error in surface area S=1.2%
We need to find the percentage error in volume V of a sphere.
Relations:
For a sphere of radius r :
‌S=4πr2
‌V=‌

4

3

πr3
Step 1: Express relative errors
For small errors,
‌‌

dS

S

=2‌

dr

r

‌‌

dV

V

=3‌

dr

r

Step 2: Connect the two
From the first equation:
‌

dr

r

=‌

1

2

‌

dS

S

Substitute into the second:
‌

dV

V

=3×‌

1

2

‌

dS

S

=‌

3

2

‌

dS

S

Step 3: Substitute given error
Error in V=‌

3

2

×1.2%=1.8%