Question

if 'r' radius of a sphere is divided into 4 equal parts.
then what is the total surface area of 4 equal parts ?​

Answer 1

Step-by-step explanation:

There has been a tacit assumption in all the answers that the sphere isn’t hollow. However, it’s interesting to note that even in the case of a hollow sphere (a spherical shell of finite thickness), the total surface of all four parts would be same as the solid sphere.

Let the thickness of the shell be t

Each of the four parts would now consist of four surfaces: a curved outer surface ( S1 ) , a curved inner surface ( S2 ) and two identical (isometric) flat surfaces ( S3 & S4 ) connecting thee inner and outer surface.

Area of surface S1 = πr2

Area of surface S2 = π(r−t)2

Area of surfaces S3 (same as that of S4 ) = 12[πr2−π(r−t)2]

So, the total surface area of one among the four parts

= Area( S1 ) +Area( S2 ) + Area ( S3 )+ Area( S4 )

= πr2+π(r−t)2+12[πr2−π(r−t)2]+12[πr2−π(r−t)2]

= πr2+π(r−t)2+[πr2−π(r−t)2]

= 2 πr2

Hence total surface area of all four parts is 8πr2 i.e. 4(2πr2)