The total surface area of a cone is A=πr2+πrl, where r is radius and l is the slant height. ‌=π(7)2+π(7)⋅√72+72‌‌[∵l=√r2+h2‌ And ‌r=7,h=7] ‌=49π+49√2π=49π(1+√2) But, the error in measuring r and h is 0.002×7=0.014 feet So, dr=0.014 and dh=0.014 Now, error in l, denoted by dl and differentiate it w.r.t r and h, we get dl=‌
∂l
∂r
dr+‌
∂l
∂h
⋅dh But l=√r2+h2 So, ‌
∂l
∂r
=‌
1
2
(r2+h2)−1∕2⋅2r=‌
r
√r2+h2
=‌
r
l
And ‌
∂l
∂h
=‌
1
2
(r2+h2)−1∕2⋅2h=‌
h
√r2+h2
=‌
h
l
So, ‌‌dl=‌
r
l
dr+‌
h
l
dh=‌
7
7√2
⋅(0.014)+‌
7
7√2
(0.014) =‌
0.014
√2
+‌
0.014
√2
=‌
2
√2
(0.014)=√2(0.014) The error in surface area, is dA, i.e., dA=‌
