Question

The radius of a circular disk is given as 21 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error in the calculated area of the disk. (Round your answer to two decimal places.) cm2 (b) What is the relative error? (Round your answer to four decimal places.) What is the percentage error? (Round your answer to two decimal places.) %

Answer 1

Answer with Step-by-step explanation:

We are given that

Radius of circular disk=r=21 cm

dr=0.2 cm

a.Area of circular disk=A=$\pi r^2$

$d A=2\pi rdr$

$d A=2\pi (21)(0.2)=8.4 \pi cm^2$

$d A=8.4\times 3.14$

Where $\pi=3.14$

$d A=26.38 cm^2$

b.Relative error=$\frac{dA}{A}=\frac{26.38}{\pi (21)^2}$

Relative error=$0.0191$

Percentage(%) error=$0.0191\times 100=1.91$%