The semi-vertical angle of a cone is `45^(@)` . If the height of the cone is 20.025, then its approximate laternal surface area, is

Options

A. `401sqrt(2) pi`
B. `400sqrt(2) pi`
C. `399sqrt(2) pi`
D. none of these

Answer

A

Explanation

Let r be the radius, h be the height and l be the slant height of a cone of semi-vertical angle `45^(@)`. Then, `r=h and l=sqrt(2h)`
`Let" " h= 20 and h+ Delta h=20.025 rArr Delta h = 0.025`
Let S be the lateral surface. Then,`S=sqrt(2) pi h^(2) " "[:' S = pirl rArr S = pih xxsqrt(2)h]`
`rArr " "(dS)/(dh)= 2sqrt2 pi h`
` ((dS)/(dh))_(h=20)=40 sqrt(2) pi`
`:." " Delta S= (dS)/(dh) Deltah rArr DeltaS=40sqrt(2)pi xx 0.025=sqrt(2)pi`
Also, at h=20, we have `S=400sqrt(2) pi`
`:." "S+DeltaS= 400sqrt(2)pi+sqrt(2)pi=401sqrt(2)pi`