Error in Radius: 3%

To find the error in the volume of a sphere, we need to understand how the volume of a sphere is calculated and how it is affected by changes in the radius.

Volume of a Sphere

The volume of a sphere is given by the formula:

V = (4/3) * π * r³

where V is the volume and r is the radius of the sphere.

Error in Volume

To calculate the error in the volume, we need to determine how changes in the radius affect the volume. Since the volume formula includes the radius cubed, even a small change in the radius can have a significant impact on the volume.

Calculating the Error

The error in the volume can be calculated using the concept of relative error. The relative error is the ratio of the absolute error to the actual value. In this case, the absolute error can be calculated by multiplying the radius by the percentage error.

Absolute Error = (3/100) * r

The relative error is then given by:

Relative Error = (Absolute Error) / (Actual Value)
= (3/100) * r / r
= 3/100

Converting the relative error to a percentage gives us the error in percentage:

Error in Percentage = (Relative Error) * 100
= (3/100) * 100
= 3%

Therefore, the error in the volume of the sphere is 3%, which corresponds to option C.