#### Question A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

#### Video Explanation

#### Explanatory Answer

Total height of toy = 15.5 cm

Radius of hemisphere = 3.5cm = \\frac{7}{2}) cm

Therefore, height of conical portion of toy = 12 cm

Surface area of toy = lateral surface area of cone + surface area of hemisphere

= πrl + 2πr^{2}, where ‘r’ is the radius (cone and hemisphere have the same radii) and ‘l’ the slant height of the cone.

Slant height of the cone, l = \\sqrt {{r}^{2}+{h}^{2}})

= \\sqrt {{\left ( {{\frac {7} {2}}} \right )}^{2}+{12}^{2}}) = \\sqrt {{\left ( {{\frac {7} {2}}} \right )}^{2}+{\left ( {{\frac {24} {2}}} \right )}^{2}})

= \\sqrt {\frac {{7}^{2}+{24}^{2}} {{2}^{2}}}) = \\sqrt {\frac {{}{25}^{2}} {{2}^{2}}}) = \\frac{25}{2}) cm

Surface area of cone = πrl = \\frac{22}{7}) × \\frac{7}{2}) × \\frac{25}{2}) = \\frac{275}{2})cm^{2}

Surface area of hemisphere = 2πr^{2} = 2 × \\frac{22}{7}) × \\frac{7}{2}) × \\frac{7}{2}) = 77 cm^{2}

Surface area of toy = \\frac{275}{2}) + 77 = 137.5 + 77 = 214.5 cm^{2}