Question

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

12 cm 15.5 cm 3.5 cm— 

Answer 1

Step 1: Find height of the cone.

the radius of the cone and the hemisphere $\left(r\right)=3.5cm$

The total height of the toy is given as $15.5cm$

So, the height of the cone $\left(h\right)=15.5-3.5=12cm$

Step 2. Find slant height $\left(l\right)$ of the cone

$$\begin{gathered} l=\sqrt{h^2+r^2} \\ =\sqrt{{12}^2+3.5^2} \\ =\sqrt{144+12.25} \\ =\sqrt{256.25} \\ =12.5cm \end{gathered}$$

Step 3: Find the total surface are of toy.

Total surface area of toy$=C.S.A$ of cone$+C.S.A$of hemisphere

$$\begin{gathered} =\mathrm{\pi rl}+2{\mathrm{\pi r}}^2 \\ =\mathrm{\pi r}(\mathrm{l}+2\mathrm{r}) \\ =\frac{22}{7}\mathrm{x}3.5(12.5+2\mathrm{x}3.5) \\ =\frac{22}{7}\mathrm{x}3.5\mathrm{x}19.5 \\ =214.5{\mathrm{cm}}^2 \end{gathered}$$

Hence, the total surface area of the toy is $214.5c{m}^2$.