Question

16) The surface area of a sphere of radius .. is (a) 216 (b) 360 (c) 616 (d)80​

Answer 1

Answer:

The volume of a circular cone is: Vc=13π⋅(rc)2⋅hVc=13π⋅(rc)2⋅h

The volume of a sphere is: Vs=43π⋅(rs)3Vs=43π⋅(rs)3

Assuming none of the metal is lost during the process of melting and recasting the two volumes are equal.

Vs=VcVs=Vc

43π⋅(rs)3=13π⋅(16)2⋅(216)43π⋅(rs)3=13π⋅(16)2⋅(216)

Solve for rsrs

(rs)3=34(13(256)(216)=13824(rs)3=34(13(256)(216)=13824

rs=13824−−−−−√3=24rs=138243=24

The area of a sphere is: A=4π⋅(rs)2A=4π⋅(rs)2

A=4π⋅(24)2=2304π≈7238.228474A=4π⋅(24)2=2304π≈7238.228474  cm2

Explanation: