#### Question

A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?

#### Solution

Given height of cone (h) = 4cm

Diameter of cone (d) = 6cm

∴Radius (r) =`6/2 =3 cm`

Let ‘l’ be slant height of cone

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

`=sqrt(3^2+4^2) =5cm`

l = 5cm

∴ Slant height of cone (l) = 5cm.

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

S_{1} = π(3)(5) = 47.1cm^{2}

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

`S_2=2pi(3)^2=56.52cm^2`

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

= 47.1 + 56.52

= 103.62cm^{2}

∴ Curved surface area of toy = 103.62cm^{2}

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#### APPEARS IN

Solution A Toy is in the Form of a Cone Surmounted on a Hemisphere. the Diameter of the Base and the Height of Cone Are 6cm and 4cm. Determine Surface Area of Toy? Concept: Surface Area of a Combination of Solids.