Answer to Question #202127 in Calculus for Ayush

Question

The dimensions of a rectangular box are measured to be 75 cm, 60 cm,and 40 cm, and each measurement is correct to within 0.2 cm .Use differentials to estimate the largest possible error when the volume of the box is calculated from these measurements.

Answer 1

volume of the box:

$V=lwh$

where $l=75$ cm is length,

$w=60$ cm is width,

$h=40$ cm is height

largest possible error:

$dV=d(lwh)=whdl+ld(wh)=whdl+l(hdw+wdh)$

where

$dl=dw=dh=0.2$ cm

then:

$dV=0.2(60\cdot40+75\cdot40+75\cdot60)=1980$ cm³