Question

In the given figure shows a toy. Its lower part is a hemisphere and the upper part is a cone. Find the volume and surface area of the toy from the measures shown in the figure ($\mathrm{\pi }=3.14$)

Answer 1

Radius of the hemisphere = Radius of the cone = r = 3 cm

Height of the cone, h = 4 cm

Let l be the slant height of the cone.

$l=\sqrt{r^2+h^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5\mathrm{cm}$

Volume of the toy = Volume of the hemisphere + Volume of the cone
$$\begin{gathered} =\frac{2}{3}\mathrm{\pi }{r}^3+\frac{1}{3}\mathrm{\pi }{r}^{2}h \\ =\frac{2}{3}\times 3.14\times {\left(3\right)}^3+\frac{1}{3}\times 3.14\times {\left(3\right)}^2\times 4 \\ =56.52+37.68 \\ =94.20{\mathrm{cm}}^3 \end{gathered}$$
Surface area of the toy = Curved surface area of cone + Curved surface area of hemisphere
$$\begin{gathered} =\mathrm{\pi }rl+2\mathrm{\pi }{r}^2 \\ =3.14\times 3\times 5+2\times 3.14\times {\left(3\right)}^2 \\ =47.10+56.52 \\ =103.62{\mathrm{cm}}^2 \end{gathered}$$
Thus, the volume and surface area of the toy are 94.20 cm³ and 103.62 cm², respectively.