XAT 2018 — QA & DI Question 7
SphereEasy
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.
Answer & solution
- A
2.2 liters
- B
2.5 liters
- C
3 liters
4 liters
- E
None of the above
Solution
Total outer surface area of a sphere of radius r = 4πr2
When the sphere is cut into 4 identical pieces, each piece will expose πr2/2 + πr2/2 = πr2 area more.
∴ Now, 4πr2 additional area needs to be painted which will require 2 more liters of paint.
∴ 4 litres of paint will be needed.
Hence, option (d).