Answer:
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
