Question

solve it ...............​

Answer 1

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;

AC2=OA2+OC2 (using pythagorean rule)⇒AC2=(3.25)2+(1.75)2⇒AC=(3.25)2+(1.75)2−−−−−−−−−−−−−−√=3.69 cm

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

  [π(1.75×3.69)+2π(1.75)2]=6.4575π+6.125π=π(6.4575+6.125)=12.5825π=39.50 cm2 ( taking π=3.14)

So the total surface area of 50 playing tops =39.50×50=1975 cm2

Therefore they had to paint 1975cm2