Question

in a solid hemisphere the circumference of circular base curved surface area and volume are in AP then possible value of radius is?​

Answer 1

Given : a solid hemisphere

the circumference of circular base  , curved surface area and volume are in AP

To Find :  possible value of radius

Solution:

Let say Radius of Hemisphere = R

circumference of circular base  = 2πR

curved surface area  = 2πR²

volume = (2/3)πR³

2πR  , 2πR²   &  (2/3)πR³   are in AP

=> ( 2πR + (2/3)πR³)  = 2 (2πR²)

Dividing both sides by 2πR

=> (  1 + (1/3)R²)  =   2R

=>    3 + R²  = 6R

=> R²  - 6R  + 3  = 0

 R = (6 ± √24)/2

=> R = 3 ± √6

possible value of radius  are 3 + √6   & 3 - √6

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