Question

The volume of a spherical cancerous tumor is given by v(r)=4/3 p r^3 .

If the radius of a tumor is estimated at 1.1 cm, with a maximum error in measurement of 0.005 cm, determine the error that might occur when the volume of the tumor is calculated.

Answer 1

Answer:

The error in the calculated volume is about $0.0242\pi \approx 0.07602 \:cm^3$

Step-by-step explanation:

Given a function y=f(x) we call dy and dx differentials and the relationship between them is given by,

$dy=f'(x)dx$

If the error in the measured value of the radius is denoted by $dr=\Delta r$, then the corresponding error in the calculated value of the volume is $\Delta V$, which can be approximated by the differential

$dV=4\pi r^2dr$

When r = 1.1 cm and dr = 0.005 cm, we get

$dV=4\pi (1.1)^2(0.005)=0.0242\pi$

The error in the calculated volume is about $0.0242\pi \approx 0.07602 \:cm^3$