The mass and density of a solid sphere are measured to be `(12.4 +-0.1)kg and (4.6 +- 0.2) kg//m^3`. Calculate the volume of the sphere with error limits .

Explanation

Here,`mpmDeltam=(12.4pm0.1)kg`
and `rhopmDeltarho=(4.6pm0.2)kgm^(-3)`
Volume, `V=(m)/(rho)=(12.4)/(4.6)=2.69 m^(3)=2.7m^(3)` (rounding off to one decimal place)
Now, `(DeltaV)/(V)=pm((Deltam)/(m)+(Deltarho)/(rho))`
or `DeltaV=pm((Deltam)/(m)+(Deltarho)/(rho))xxV=pm((0.1)/(12.4)+(0.2)/(4.6))xx2.7`
`pm0.14`
`therefore` `VpmDeltaV=(2.7pm0.14)m^(3)`