A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm respectively.The radii of the hemispherical and conical parts are the same as that of the cylindrical part.Find the surface area of the toy if the total height of the toy is 30 cm.

#### Solution

S_{1} = 2π(2)(13)

S_{1} =408.2cm^{2}

Curved surface area of cone(S_{1}) = πrl

Let l be slant height of cone

`l=sqrt(r^2+h^2`

h = 30 - 13 - 5 = 12cm

⇒`l=sqrt(12^2+5^2)` = 13cm

l = 13cm

∴Curved surface area of cone(S_{2}) = π(5)(13)

= 204.1cm^{2}

Curved surface area of hemisphere(S_{3}) = 2πr^{2}

= 2π(5)^{2}

= 2π(25) = 50π = 157cm^{2}

Total curved surface area(S) = S_{1 }+ S_{2} + S_{3}

S = 408.2 + 204.1 + 157

S = 769.3cm^{2}

∴ Surface area of toy(S) = 769.3cm^{2}