Answer with Step-by-step explanation:
We are given that
Radius of circular disk=r=25 cm
Maximal error in measurement of radius =[tex]\Delta r=[/tex]0.3
We know that
Surface area of circle =A=[tex]\pi r^2[/tex]
Differentiate w.r.t r
a.Maximum error=[tex]dA=2\pi rdr[/tex]
Substitute the values then we get
[tex]dA=2\times 3.14\times 25\times 0.3=47.1 cm^2[/tex]
Hence, the maximum error in area of disk=[tex]47.1 cm^2[/tex]
b.
Relative error in A: [tex]\frac{\Delta A}{A}=\frac{2\pi r\Delta r}{\pi r^2}[/tex]
Substitute the value in the formula
Then ,we get
Relative maximal error in area of disk=[tex]\frac{2\cdot 25}{(25)^2}(0.3)=0.024[/tex]
Hence, the relative maximum error in area of disk=0.024
c.Relative error percentage in area of disk=[tex]\frac{\Delta A}{A}\times 100[/tex]
Substitute the values then we get
Relative error percentage in area of disk=[tex]0.024\times 100=2.4[/tex]%
Hence, the percentage error in area of disk=2.4%
