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A toy is in the form of a cylinder of diameter 2 2 m and height 3.5 m surmounted by a

cone whose vertical angle is 60. Find total surface area of the top

Total Surface Area = C.S.A. of cylinder + Area of the base of the cylinder + L.S.A. of the cone

Now the vertical angle of the cone is 60 degrees.

Therefore, The base angles should be 60 degrees each.

Diameter of the circular end = Slant height of the cone = 2.2 m

Now T.S.A. = 2*22/7*1.1*3.5 + 22/7*1.1*1.1 + 22/7*1.1*2.2

                     = 24.2 + 3.803 + 7.606 = 35.609 m2 

Therefore the total surface area of the toy is 35.609 m2 .

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Total Surface Area = C.S.A. of cylinder + Area of the base of the cylinder + L.S.A. of the cone

Now the vertical angle of the cone is 60 degrees.

Therefore, The base angles should be 60 degrees each.

Diameter of the circular end = Slant height of the cone = 2.2 m

Now T.S.A. = 2*22/7*1.1*3.5 + 22/7*1.1*1.1 + 22/7*1.1*2.2

= 24.2 + 3.803 + 7.606 = 35.609 m2

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Let the radius of the cylinder is r and slant height of the cone is l, and height of the cylinder is h =3.5m.
As vertical angle is 60, Hence angle FAC = 60/2 =30
So In triangle FAC , we have
sinA = CF/AC = root2/AC
Sin30 = root2/AC
AC = 2root2

So surface area of the toy :
Curved Surface area of cylinder + Curved surface area of cone + surface area of the circular base
= 2(pi)rh + (pi)rl + (pi)r2 
= 2(3.14) (root2) (3.5)  + (3.14) (root2)(2root2) + (3.14)(root2)2
= 44.67m2
Hence the total surface area of the toy is 44.67m 2
Hope it is right!
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