A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius.

Solution:

Let r and h be the radius of cone, hemisphere and height of cone

$\therefore \mathrm{h}=(15.5-3.5) \mathrm{cm}$

$=12.0 \mathrm{~cm}$

Also $\ell^{2}=\mathrm{h}^{2}+\mathrm{r}^{2}$

$=12^{2}+(3.5)^{2}$

$=156.25$

$\therefore \ell=12.5 \mathrm{~cm}$

Curved surface area of the conical part $=\pi r \ell$

Curved surface area of the hemispherical part $=2 \pi \mathrm{r}^{2}$

Total surface area of the toy $=\pi \mathrm{r} \ell+2 \pi \mathrm{r}^{2}$

$=\pi \mathrm{r}(\ell+2 \mathrm{r})$

$=\frac{\mathbf{2 2}}{\mathbf{7}} \times \frac{\mathbf{3 5}}{\mathbf{1 0}}(12.5+2 \times 3.5) \mathrm{cm}^{2}$

$=11 \times(12.5+7) \mathrm{cm}^{2}=11 \times 19.5 \mathrm{~cm}^{2}$

$=214.5 \mathrm{~cm}^{2}$