a manufacturer involved 10 children in colouring playbg top which is shaped like a cone surmounted by a hemisphere . the entire top is 5cm in heigh and the diameter of the to is 3.5cm . find the area they had to paint if 50 playing tops wee given to them.

(a) how is child labour an abuse gfor the society?

(b)what steps can be taken to abolish child labour?

The colouring playing tops are shown above i.e. cone surmounted by a hemisphere.
Here AD represents the height of entire top i.e. AD = 5 cm
Diameter = BC = 3.5 cm
So radius = OB = OC = OD = 1/2(BC) = 1.75 cm
So height of cone = OA= AD - OD = 5 - 1.75 = 3.25 cm

Now from right triangle AOC we have;
$$\begin{gathered} A{C}^2=O{A}^2+O{C}^2 (u\sin g pythagorean rule) \\ \Rightarrow A{C}^2={\left(3.25\right)}^2+{\left(1.75\right)}^2 \\ \Rightarrow AC=\sqrt{{\left(3.25\right)}^2+{\left(1.75\right)}^2}=3.69 cm \end{gathered}$$
So the slant height of the cone = 3.69 cm
 Now total surface area of each playing top
  = Curved surface area of cone + curved surface area of hemisphere
  $$\begin{gathered} \left[\mathrm{\pi }\left(1.75\times 3.69\right)+2\mathrm{\pi }{\left(1.75\right)}^2\right] \\ =6.4575\mathrm{\pi }+6.125\mathrm{\pi } \\ =\mathrm{\pi }\left(6.4575+6.125\right) \\ =12.5825\mathrm{\pi } \\ =39.50 {\mathrm{cm}}^2 ( \mathrm{taking} \mathrm{\pi }=3.14) \end{gathered}$$

So the total surface area of 50 playing tops $=39.50\times 50=1975 c{m}^2$
Therefore they had to paint $1975c{m}^2$ .