If errors of 1% each are made in te base radius and height of a cylinder, then the percentage error in its volume, is

Options

A. `1%`
B. `2%`
C. `3%`
D. none f these

Answer

C

Explanation

Let V be the volume of the cone of base radius r and height h. Then,
`V=pir^(2) h`
`rArr " "dV=d(pir^(2) h)`
`rArr dV=pi(h" "dr^(2)+ r^(2) dh)`
`rArr" "dV=pi(2rhdr+r^(2)dh)`
`rArr" "(dV)/V= (pi2rh" "dr+r^(2)dh)/(pir^(2)h)`
`rArr" "(dV)/V=2/rdr+(dh)/h`
`(dV)/V xx100=2(dr)/rxx100+(dh)/h xx100`
`rArr" "(DeltaV)/V xx100=2 ((Delta r)/r xx100)+((Deltah)/h xx 100)2 xx1+1=3`