The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. (8 pts) a) Use differentials to estimate the maximum error in the calculated area of the disk. b) What is the relative error

the maximum error in the calculated area of the disk ΔA = 9.6 π cm²

Relative error = 0.016667

Step-by-step explanation:

Given that:

The radius of a circular disk is given as 24 cm with a maximum error in measurement 0f 0.2 cm.

The objective of this question is to use differentials to estimate the maximum error in the calculated area of the disk and determine the relative error.

To start with the differentials used to estimate the maximum error in the calculated area of the disk; we have:

radius of a circular disk  r = 24 cm

maximum error of measurement Δr = 0.2 cm

By the area of a circular disk ; A = πr²

Hence, the error in measuring the area can be represent by the equation;

ΔA = 2πrΔr

ΔA = 2×π ×(24)× (0.2)

ΔA = 9.6 π cm²

The relative error can be determined by using the expression;

Relative error = ΔA /A

where;

ΔA = 2πrΔr and A = πr²

Relative error = 2πrΔr/πr²

Relative error = 2rΔr/r²

Relative error = 2Δr/r

Relative error = 2×0.2/24

Relative error = 0.4/24

Relative error = 0.016667

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step-by-step explanation:

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