XAT 2012 — QA & DI Question 9
Answer the following question based on the information given below.
The following graphs shows the revenue (in $ million) of three companies in their initial six years of operations, in an economy which is characterized by a persistent inflation.
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A spherical metal of radius 10 cm is molten and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by:
Answer & solution
- A
1000 times
- B
100 times
- C
10 times
- D
No change
None of the above
Let r be the radius of the smaller sphere.
Now, the volume of the big sphere and the 1000 small spheres is same.
Hence, we have,
Hence, r3 = 1
Hence, r = 1
Now, total surface area of big sphere = 4 × π × 102 = 400π
Total surface area of 1000 new sphere = 1000 × 4π × 12 = 4000π
Hence, total surface area increases by, (4000π – 400π) / 400π = 9 times.
Hence, option (e).