the radius of a ball was measured and found to be 25 \text{ cm} with a possible error in measurement of at most 0.01 \text{ cm}. what is the maximum error in using this value of the radius to compute the volume of the ball?



Answer :

The maximum error in volume of ball is ± 235.619 cm³

What  is maximum error?

The margin of error, also known as the maximum error of estimation, is equal to one-half the breadth of a confidence interval and serves as a measure of how accurate an estimate is.

The formula for the confidence limits on can be written as follows: where is half of the confidence interval's breadth.

Volume of ball is given by:

V =  (4/3)πr³

Change in volume (ΔV) = (4/3)π × 3r² (Δr)

= 4π × 3r² (Δr)

= 4π × 3* 25² (±0.01)

= ± 235.619 cm³

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