• # question_answer 2) 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.

 Given, radius of base $r=3.5\text{ }cm$ Total height of toy $=15.5\text{ }cm$ Height of cone $'h'=15.5-3.5$ $=12cm$ Slant height $'l'=\sqrt{{{h}^{2}}+{{r}^{2}}}$ $=\sqrt{{{12}^{2}}+{{3.5}^{2}}}$ $=\sqrt{144+12.25}$ $=\sqrt{156.25}$ $=12.5\,\,cm$ Total S.A. of toy = CSA of cone + CSA of hemisphere $=\pi rl+2\pi {{r}^{2}}$ $=\pi r\,[l+2r]$ $=\frac{22}{7}\times 3.5[12.5+2\times 3.5]$ $=22\times 0.5[12.5+7]$ $=11\times 19.5$ $=214.5\,\,c{{m}^{2}}$