The curved surface area of a hemisphere of radius 6cm is equal to 2/5 of the curved surface area of a cone of radius 12cm.Find the volume of the cone.

A)1357.71cm^3

B)1022.38cm^3

C)1252.61cm^3

D)2039.68cm^3

Asked by adalroshan2464 | 17th Nov, 2018, 05:56: PM

Expert Answer:

Curved surface area of hemisphere = 2πr2 = 2×π×6×6 = 72π cm2
Curved surface area of cone whose radius R and height h = begin mathsize 12px style pi cross times R cross times square root of R squared plus h squared end root space end style
It is given that (2/5)th of curved surface area of cone  is curved surface area of hemi-sphere .
 
begin mathsize 12px style 72 pi space equals space 2 over 5 pi cross times 12 cross times square root of 12 squared plus h squared end root space........... left parenthesis 1 right parenthesis end style
solving eqn.(1) for h, we get h = 9 cm
 
Volume of cone = begin mathsize 12px style 1 third pi space R squared space h space equals space 1 third straight pi cross times 12 cross times 12 cross times 9 space equals space 1357.17 space cm cubed end style

Answered by Thiyagarajan K | 17th Nov, 2018, 10:12: PM

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