A play-top is in the form of a hemisphere surmounted on a cone. The diameter of the hemisphere is 3.6 cm. The total height of the play-top is 4.2 cm. Find its total surface area.

A play-top is made up of a hemisphere (at the top) and cone(at the bottom).

Given, Diameter of the hemisphere = 3.6 cm

Radius of the hemisphere =

= 1.8 cm

Total height of the play-top = 4.2 cm

Height of cone = (Total height of the play-top)-( Radius of the hemisphere)

⇒ Height of cone = 4.2-1.8

= 2.4 cm

Now, Total surface area of play-top = Lateral surface area of hemisphere+ Lateral surface area of cone

Lateral surface area of hemisphere = 2r²

= 21.81.8

= 6.48

Lateral surface area of cone = rl ,

where l =

⇒ l =

⇒ l =

⇒ l =

⇒ l = 3

So, Lateral surface area of cone = 1.83

= 5.4

Total surface area of play-top = 6.48+5.4

= 11.88 cm²

Total surface area is 11.88 cm².