Question

A cone of height 12m and base radius 6m cut from the top at a 4m find the surface area of remainng

Answer 1

In Δ ABE and Δ ACD,

BE || CD

So, Δ ABE ∼ Δ ACD 

=> AB/AC = BE/CD

=> 4/12 = BE/6

=> 1/3 = BE/6

=> 1 = BE/2

=> BE = 2

Now, AD2 = AC2 + CD2 

=> AD2 = 122 + 62 

=> AD2 = 144 + 36

=> AD2 = 180

=> AD = √180

=> AD = 13.42

Now, total surface are of complete cone = πr(l + r)

                      = π*6(6 + 13.42)

            = π*6*19.42

              = 3.14*6*19.42

            =  365.87 

Now, curved surface area of smaller cone of height 4 m and radius 2 m = πrl

From the figure,

      l = √(AC2 + CD2 )

=> l = √(42 + 22 )

=> l = √(16 + 4)

=> l = √20

=> l = 4.47

So, the curved surface are = πrl = 3.14*2*4.47 = 28.08

Now, Total surface area of the remaining cone = totalsurface are of bigger cone - curved surface area of smaller cone + area of base of smaller cone

               = 365.87 -28.08 + π*2*2

                   = 365.87 - 28.08 + 3.14*4

          = 365.87 - 28.08 + 12.56
=350.35 m2 

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