If three solid spheres of metal whose radii are 1 cm, 6 cm and 8 cm are melted to form another solid sphere, then the surface area of new sphere (in cm2) is:

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SSC GD Constable (2022) Official Paper (Held On : 08 Feb 2023 Shift 1)
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  1. 364 π
  2. 243 π
  3. 324 π
  4. 642 π

Answer (Detailed Solution Below)

Option 3 : 324 π
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Detailed Solution

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Given:

Radii of the initial spheres (R1, R2, R3) = 1 cm, 6 cm, 8 cm

Formula used:

The volume of a sphere = 4/3 × π × r,

The surface area of a sphere  = 4 × π × r2,

where r is the radius of the sphere.

Calculation:

Volume of the new sphere = Total volume of all the three initial spheres

Volume =  4/3 × π × (R13 + R23 + R33)

Volume = 4/3 × π × (1 + 216 + 512)

Volume = 972 π cm3

4/3 × π × r= 972 π 

Hence, radius of new sphere is 9 cm.

Now putting this value in surface area formula,

Surface area of the new sphere  = 4 × π × (9)= 324 π cm2

∴ The surface area of the new sphere is 324 π cm2.

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