If an error of `1^(@)` is made in measuring the angle of of a sector of radius 30 cm, then the approximate eror in its area, is

Options

A. `450 cm^(2)`
B. `25 pi cm^(2)`
C. `2.5 pi cm^(2)`
D. none of these

Answer

C

Explanation

Let A be the area and `theta` (in radians) be the sector angle. Then, ` A=1/2 xx30^(2) xx theta" "[:' A=1/2r^(2) theta]`
`rArr" "(dA)/(d theta) =450` Let `Delta theta` be an error in theta and Delta A be the corresponding error in A. Then,
`Delta A=(dA)/(d theta) Deltatheta`
`rArr" "DeltaA=450 xxpi/180" "[:'Delta theta = 1 ^(@)= pi/180 radians]`
`rArr" "DeltaA = 2.5pi cm^(2)`