#### To determine

**To estimate:** The maximum error in the calculated area of circular disk.

#### Answer

The maximum error in the area of the circular disk is ΔS≈9.6π cm2.

#### Explanation

**Given:**

The radius of the circular disk is 24 cm and the maximum error in measurement is 0.2 cm.

**Calculation:**

Suppose *r* be a radius of the circle.

Note that, the area of the circular disk is S=πr2.

The differential is dS=f′(r)dr (1)

Derivative of the function f(r)=πr2 is f′(r)=2πr,

Substitute f′(r)=2πr in equation (1),

dS=2πrdr

Substitute r=24 and dr=0.2,

dS=2π(24)(0.2)=9.6π cm2

The maximum error in the area of the circular disk is ΔS which is approximately same as dS.

Therefore, the maximum error in the area of the circular disk is ΔS≈9.6π cm2.

#### To determine

**To find:** The relative error and percentage error.

#### Answer

The relative error and the percentage error are 0.016¯ and 1.6¯% respectively.

#### Explanation

**Calculation:**

The relative error is computed by dividing the change of the area (ΔS) with the area *S*.

That is, the relative error is ΔSS.

Note that, the value ΔS is approximately equal to dS.

ΔSS≈dSS=2πrdrπr2=2drr

Substitute r=24 and dr=0.2,

ΔSS≃20.224=0.016¯

Therefore, the relative error is 0.016¯*.*

Note that, the percentage error is the product of the relative error and 100.

The percentage error is computed as follows,

Percentage error=0.016¯×100%=1.6¯%

Therefore, the percentage error is 1.6¯%.