Question

What is the percentage error in the volume of a cube when error in measuring its side is 2%?

Answer 1

volumeof cube =side^3
therefore total percentage error would be 3* error in 1 side
so answer is 3*2=6
i thin it is correct..

Answer 2

hey there !!!

=) let us consider the cube of side "a "

here given ∆a/a ×100 = 2%

◆ Volume (v) = a^3

=) v = a^3

taking log both sides ,

=) log v = log a^3

=) log v = 3log a [ "," log m^n = n log ]

differentiate both sides ,

=) dv/ v = 3 da/a --------(2)

we can assume dv = ∆v

so equation (2) becomes..

=) ∆v/v = 3 ∆a/a

multiplying by 100 both sides , we get

=) ∆v/v ×100 = 3 (∆a/a ×100)

here given that : ∆a/a ×100 = 2%

now ,

=) ∆v/v ×100 = 3 ×2 = 6%

so % error in volume is 6% ans ..