Question

An egg of a particular bird is very nearly spherical. The radius to the inside of the shell is 4 millimeters and the radius to the outside of the shell is 4.2 millimeters. Use differentials to approximate the volume of the shell. [Remember that V(r) = 4/3 pi r^3, where r is the radius.] The volume of the shell is approximately mm^3.

Answer 1

Answer: The volume of shell is 12.8π mm².

Step-by-step explanation:

Since we have given that

Radius to the inside of the shell = 4 milimeters

Radius to the outside of the shell = 4.2 milimeters

Since r changes from 4 mm to 4.2 mm

so, $dr=4.2-4=0.2\ mm$

As we know that

Volume of shell is given by

$\dfrac{4}{3}\pi r^3$

$dv=\dfrac{4}{3}\pi 3r^2\ dr\\\\dv=4r^2\pi\ dr\\\\dv=4(16)\times 0.2\pi\\\\dv=12.8\pi$

So, the volume of shell is 12.8π mm².