Error % is add when it is in multiple and division

so error in radius =1%
...
error in volume = 4πr³= here 4 and π are constant ...error is only in r so 1+1+1=3% error in volume

Introduction:
The error in the measurement of the radius of a sphere will affect the calculated value of its volume. In this scenario, the error in the radius measurement is given as 1%. We need to determine the corresponding error in the calculated volume.

Formula for Volume of a Sphere:
The volume of a sphere is given by the formula V = (4/3)πr^3, where V is the volume and r is the radius.

Error Propagation:
To calculate the error in the volume, we need to consider how the error in the radius propagates through the formula for volume.

Percentage Error:
The percentage error in a quantity is given by (Error / Measurement) * 100.

Calculating the Error in Volume:
Let's assume the measured radius of the sphere is r and the measured volume is V.

1. Percentage Error in Radius:
The given error in the radius measurement is 1%. Therefore, the percentage error in the radius is 1%.

2. Error in Volume:
To calculate the error in the volume, we need to differentiate the volume formula with respect to the radius:
dV/dr = 4πr^2

3. Percentage Error in Volume:
The percentage error in the volume can be calculated using the formula:
(Percentage Error in Volume) = (Percentage Error in Radius) * (dV/dr)

Substituting the values:
(Percentage Error in Volume) = 1% * (4πr^2)

4. Simplifying the Percentage Error in Volume:
To simplify the percentage error, we can express the radius in terms of the volume formula. From the volume formula, we have:
r = (3V / (4π))^(1/3)

Substituting this value into the percentage error formula, we get:
(Percentage Error in Volume) = 1% * (4π((3V / (4π))^(1/3))^2)

Simplifying further, we have:
(Percentage Error in Volume) = 1% * (4π(27V^2 / (16π^2))^(1/3))

By canceling out the π and simplifying the expression, we find:
(Percentage Error in Volume) = 1% * (3(27V^2 / 16π^2)^(1/3))

5. Final Answer:
The error in the calculated value of the volume is 3% (option B) when the error in the measurement of the radius is 1%.