Question
Download Solution PDFIf 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radii of the initial spheres (R1, R2, R3) = 1 cm, 6 cm, 8 cm
Formula used:
The volume of a sphere = 4/3 × π × r3 ,
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 × r3 = 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)2 = 324 π cm2
∴ The surface area of the new sphere is 324 π cm2.
Last updated on Jun 30, 2025
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