A toy is in the form of a cone mounted on a hemisphere of radius $\displaystyle 7$ cm. The total height of the toy is $\displaystyle 31$ cm. Find the total surface area of the toy.

Height of conical part \(\displaystyle =31-7=24 \mathrm{~cm}\) Slant height of conical part \(\displaystyle =\sqrt{(7)^{2}+(24)^{2}}=25 \mathrm{~cm}\) TSA of the toy = CSA of conical part + CSA of hemispherical part \[\begin{aligned} & =\frac{22}{7} \times 7 \times 25+2 \times \frac{22}{7} \times 7 \times 7 \\ & =858 \mathrm{~cm}^{2} \end{aligned} \] So, the total surface area of the toy is \(\displaystyle 858 \mathrm{~cm}^{2}\).