It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces. ?->(Show Answer!)

1. It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces.

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By: anil on 05 May 2019 02.34 am

2 litres are required to paint the surface of a solid sphere.
Surface area of the solid sphere = $$4pi*r^2$$
Now, the solid sphere is cut into 4 identical parts. This is possible only when the sphere is cut into 4 quarter spheres.
After making the first cut, 2 hemispheres will be formed. 2 circles of area $$pi*r^2$$ will get exposed in addition to the surface area of the sphere (the base surface of the bottom hemisphere and the base of the top hemisphere).
Now, another perpendicular cut will be made along the diameter of the sphere. 2 additional surfaces will get exposed again (one on left hemisphere and the another on the right hemisphere).

Area exposed after making 4 identical pieces = $$4*pi*r^2$$ + $$2*pi*r^2$$ + $$2*pi*r^2$$
= $$8*pi*r^2$$
2 litres of paint is required to paint an area of $$4pi*r^2$$
=> 4 litres of paint will be required to paint an area of $$8*pi*r^2$$.

Therefore, option D is the right answer.

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