Question : A metallic solid spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 2 cm and 1.5 cm. What is the surface area (in cm2) of the third ball?
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution :
Let the radius of the smaller balls be r
1
, r
2,
and
r
3.
The radius of the larger sphere is r.
So,
⇒ r
3
= r
1
3
+ r
2
3
+ r
3
3
⇒ 3
3
= 2
3
+ 1.5
3
+ r
3
3
⇒ 3
3
= 8 + 3.375 + r
3
3
⇒ r
3
3
= 27 – 8 – 3.375
⇒ r
3
3
= 15.625
⇒ r
3
= 2.5
The surface area of the third ball = 4
= 4
= 25
Hence, the correct answer is
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