Question

If the percentage error in measurement of radius of a sphere is 0.2%. Calculate the percentage error in volume.

Answer 1

Given :-

• percentage error in radius (r) of sphere = 0.2 %

To find :-

• percentage error in Volume(V) of sphere

Knowledge required :-

Error in case of a measured quantity raised to a power

In General, if Z = Aᵇ

then, ΔZ / Z = b ( Δ A / A)

Hence, the rule is : The relative error in a physical quantity raised to a power k is the k times the relative error in the individual quantity.

Solution :-

Given that

→  Percentage error in radius (r) = 0.2 %

that is

→ (Δ r / r )×100  = 0.2 %   ....equation(1)

Now,

As we know

→ Volume of sphere = 4/3 π r³

In the formula for calculating Volume 4/3 and π are constant .hence , there is no chance of any effect of these constant values on the error in Volume of  sphere , so we can say that Error in volume of sphere is dependent on cube of radius of sphere only. so,

Using the rule for error in case of quantity raised to a power

→  Δ V / V = 3 ( Δ r / r )

multiplying by 100 % both sides

→ (Δ V / V) × 100% = 3(Δr / r) × 100%

using equation (1)

→ (Δ V / V) × 100% = 3 ( 0.2 )

→ (Δ V / V) × 100 = 0.6 %

Hence , the percentage error in Volume of sphere will be 0.6 % .

Answer 2

Answer:

THE CORRECT ANSWER IS 0.6% SURELY